NEW ORLEANS -- Marcus Peters leaped, but the ball sailed over his fingertips, just out of reach.

Drew Brees completed a 72-yard pass to Michael Thomas for a touchdown late and effectively ended the Los Angeles Rams' perfect record and comeback bid, as the Rams fell to the New Orleans Saints 45-35 at the Superdome.

"With how good this team is, we don't ever think this day will come because we fight so hard together," Peters said, when asked about the Rams' first loss. "We know all three phases, we're going to go out there and compete, that's why we came back at the end of the game."

The Rams found themselves in a hole early, as the Saints went on a 21-3 run to close out the first half, and led 35-17. But out of the break, the Rams scored 18 unanswered points to tie the score at 35 with 9:57 remaining in the game.

"We're good," coach Sean McVay said after the game. "We love it. You find about yourself when you have a little bit of adversity. I know everybody in that locker room is going to respond the right way and sometimes setbacks can be set ups for comebacks."

Entering Sunday's game, the Rams were the lone remaining undefeated team in the NFL, after their first 8-0 start since 1969.

Defensive lineman Michael Brockers expressed relief that the team would no longer be burdened with the talk of a perfect season.

"The pressure is off," Brockers said. "No more media, we're the great team, nobody can beat us. ... The pressure is off."

Sunday's game was just the second time in McVay's two seasons as coach that the Rams fell behind by 21 or more points. The other instance was Week 17 last season, when McVay decided to rest his starters in preparation for the playoffs.

A come-from-behind victory against the Saints would have served as the Rams' third-biggest comeback in franchise history. Instead, the Rams have been unable to overcome a 21-point deficit since Week 12 of the 2005 season against the Houston Texans. They've lost 49 straight when trailing by 21 points or more, according to ESPN Stats & Information.

"It's a loss," Rams defensive tackle Aaron Donald said. "Nobody likes to lose, so we just got to watch the film and fix it. We ain't panicking, we ain't worried. We just got to be better."

In the first half, the Rams' defense had few answers for Brees, as the NFL's all-time leading passer helped the Saints to 313 total yards of offense and passed for three touchdowns, as Alvin Kamara rushed for two more.

The Rams appeared to get the first break after both teams scored on their first two possessions.

Outside linebacker Samson Ebukam forced a fumble that was recovered by Donald.

But the offense stalled and the field goal unit came on. A fake field goal attempt resulted in punter Johnny Hekker rushing for 3 yards before he was knocked out of bounds, 1 yard short of a first down.

"We're an aggressive attacking-type team and we if we feel like some of these looks present themselves to try to do that," McVay said. "We have confidence in our players. Unfortunately it didn't work out in that situation."

After Hekker was stopped short, momentum shifted.

The Saints scored a touchdown on the ensuing series, and Greg Zuerlein followed with a missed field goal attempt from 51 yards. The Saints scored again, and it appeared the Rams would have the chance to close out the half.

But Goff threw an interception, his sixth of the season, with 1:08 to play in the half and the Saints converted the takeaway into another touchdown to take a 35-14 lead.

Zuerlein closed the half with a 56-yard field goal, and the Rams trailed 35-17, as they became the first team to start the season 8-0 or better and allow at least 35 points in a half, according to the Elias Sports Bureau.

In the second half, the Rams went on an 18-0 run, as Malcolm Brown caught a short pass and fought his way to an 18-yard touchdown, Cooper Kupp caught a 41-yard pass for a touchdown and Zuerlein made a 34-yard field goal.

But with four minutes remaining, Brees shut the door with the deep touchdown pass on 3rd and 7 from his own 28-yard line.

"He just beat me off the line, looked back and tried to make a play on the ball," Peters said. "I got beat."

Brees finished 25-of-36 for 346 yards and 4 touchdowns. Thomas caught 12 passes for 211 yards and a touchdown as he set a new franchise record for the most receiving yards in Saints history.

"This game right here might be a blessing in disguise. We came out, we fought back, so you never see us fold," Brockers said. "It will help us play a little bit better. It will help us play a little bit looser, too."