With the Border-Gavaskar Trophy just two wickets away from being back in their grasp, it will take a reversal in form as unforeseen as history's most fiendish twists to prevent India rolling on to an unprecedented Test series triumph in Australia.

Only torrential rain could deny India a win on Sunday when they return for day five of this third Domain Test – with Australia notionally needing 141 extra runs – and India's performance here has only enhanced the likelihood they will achieve an outcome that has eluded them for seven decades.

And one that skipper Virat Kohli has so publicly coveted from the moment his men arrived in Sydney last month.

More symbolically, it will highlight the yawning gulf between the world's top-ranked Test team and an Australia outfit currently listed fifth, with a real danger of slipping further after their upcoming two-Test series against sixth-ranked Sri Lanka starting next month.

The fragility and skittishness so often associated with India sides in the hostile Australian cricket climate has been glaringly absent among Kohli's charges.

The manner in which they set up inevitable victory in the one-sided third Test today bore characteristics more often attributed to Australia teams at home.

They were patient, disciplined, selfless and utterly ruthless in playing the game on their terms from the moment that Kohli won the toss, and in exploiting the numerous frailties in their outclassed and less-experienced opponents.

No finer example exists of the clinical India than seamer Jasprit Bumrah, who has emerged as the feared fast-bowler his nation has so sought and one who can adapt his considerable skills to any playing surface around the globe.

By contrast, the comfort and confidence that Australia took from their stirring second Domain Test win in Perth less than a fortnight ago dissipated in the dark cloud of two sub-par batting efforts.

As well as the frustration and fatigue that came from toiling with the ball on all four days, only to see India declare both their batting innings such was their superiority.

The lone light was the all-round contribution of Pat Cummins, who followed career-best bowling figures (6-27) in India's second innings by then compiling his highest Test score with the bat, an unbeaten 61 in his team's stumps score of 8-258.

It will therefore take a plot shift even more dramatic than that which shaped this Test when wickets suddenly started tumbling, to stop India surging to victory tomorrow and holding on in the fourth Domain Test that starts in Sydney next Thursday.

A match that Australia enters facing serious scrutiny on several fronts.

Aaron Finch's future as a Test opener hangs by a thread, and it appears that only Australia's decision to name their squad for both the Melbourne and Sydney matches will prevent a revamp of an ineffective top-order.

It was not so much that Finch, who went into his first home-town Test nursing a damaged finger, produced his second single-figure of the match but rather the manner in which he surrendered his wicket in the second over of Australia's salvage mission today.

A ball after surviving a raucous shout for lbw, Finch wafted at a shorter, wider delivery from Bumrah in the manner that coaches employ to drill their slips fielders.

And it was with that same perfunctory air that Kohli claimed the catch in front of his face.

Finch's less travelled opening partner Marcus Harris again looked more solid in the role, until India reverted to spin in the sixth over and the same shortcoming that has haunted Australia's batters in recent years was exposed in the left-hander.

Reaching for the ball in advance of his leading leg – the quintessence of the 'hard hands' that has so often undone touring teams in Asia – Harris squeezed a sharply spinning delivery from Ravindra Jadeja to the fielder crouched at bat-pad.

As was the case in Australia's inadequate first innings, Usman Khawaja seemed as untroubled as any batter held such right on the contentious surface and, briefly, lit a faint hope that defeat might be stayed.

Certainly, the left-hander's timing in the three boundaries and an exquisite straight six he struck from Jadeja suggested he might somehow quarantine himself against the day-four variations in bounce.

That was exposed as fallacy when he copped a delivery from Mohammad Shami that hurried through and kept a touch low, ensuring the ball missed Khawaja's bat.

The India seamers around-the-wicket line of attack against Australia's surfeit of left-handers was proving productive, as Shaun Marsh fell in similar circumstances to Khawaja less than an hour later.

Marsh could consider himself stiff, having negotiated more deliveries (72) than any other specialist Australia batter in the Test to that point, only to be adjudged lbw by umpire Marais Erasmus to a delivery that looked to be sliding down leg side.

However, while Marsh's call for review confirmed that initial suspicion, the fact it had been adjudged out on the field meant the decision was upheld and – at 4-114 midway through day four – pursuit of either victory or a draw was clearly futile.

The surrender was formally signalled when Mitchell Marsh flayed at an inviting delivery drifted up by Jadeja, to which he tamely produced a sliced drive to an exultant Kohli at extra-cover.

It was a shot in keeping with the younger Marsh's clear ploy to take that attack to India's spinner, an over after he had lifted Jadeja beyond the mind-on fence.

But so soft did that capitulation appear, it armed Marsh's already brimming army of critics with further fuel in their calls for him to be fired.

When Travis Head, Australia's leading run scorer for the series in addition to being the youngest of a hardly battle-hardened top six, dragged-on aiming a cover-drive that was at once instinctive as well as ill-advised, the crowd sensed India were home.

Those who have been studying Australia's batting more closely, however, understood that the fall of the sixth wicket merely united their most defiant pair – Paine and Cummins.

So it was that the skipper and the seamer, both of whom have spent more time running up and down the maligned Melbourne pitch than any other Australia players in this Test, hung tough for more than 20 overs.

The last line of resistance was then broken an hour before stumps were scheduled.

Paine feathered a tough catch to his rival keeper Rishabh Pant, with whom he has been engaging a running verbal dissertation over the past four days, and the result that seemed so distant after the first two, tawdry days was remarkably nigh.

And with showers tipped for Sunday morning, India became desperate to close it out.

Having woken to heavy cloud and stubborn rain today, and with forecasts suggesting more of Melbourne's infamously Manchester weather due on Sunday, they had started day four seeking quick runs.

The challenge of surviving for any length of time on such a fraught pitch became apparent in Cummins' opening over of the morning.

Pant aimed an airy drive at a delivery that kept low and took an under edge, the chance barely clipping Paine's gloves as he launched full length to his right.

It was suitable signal for the visitors to hit out lest they got out, and opener Mayank Agarwal responded by launching a pair of sweetly struck sixes over spinner Nathan Lyon's head with a disdain that belied the pitch's erratic nature.

The rationale for such urgency was vindicated shortly after when Agarwal, as assured as any batter in this Test despite it being his maiden match, leapt in the air to combat a short ball from Cummins that, instead, hit the bat's toe and took the stumps.

The muted Australia celebrations that greeted Cummins' first five-wicket haul on home turf confirmed what the manner of Agarwal's dismissal meant for those luckless batters to follow.

A flurry of shots – some of which connected, others that were entertainingly speculative – ensued over the next half hour before Pant's removal – the ball after he had clubbed Josh Hazlewood for a clinical straight six – convinced Kohli he was sufficiently in surplus.

The declaration 398 runs in front gifted his bowlers a minimum of 167 overs – essentially the same timeframe as India's epic first innings had occupied – and five-and-a-half sessions to retain the Border-Gavaskar Trophy.

As well as carry them to the cusp of history.

Australia XI: Aaron Finch, Marcus Harris, Usman Khawaja, Shaun Marsh, Travis Head, Mitchell Marsh, Tim Paine (c), Pat Cummins, Mitchell Starc, Nathan Lyon, Josh Hazlewood

India XI: Virat Kohli (c), Ajinkya Rahane, Mayank Agarwal, Hanuma Vihari, Cheteshwar Pujara, Rohit Sharma, Rishabh Pant, Ravindra Jadeja, Mohammed Shami, Ishant Sharma, Jasprit Bumrah