Wil Lutz kicked a 44-yard field goal with 21 seconds left, Cleveland kicker Zane Gonzalez pushed the second of his two missed field goals wide right in the final seconds, and the Saints held on for a 21-18 victory that extended the Browns' winless streak to 19 games.
''These are games that we find we find our identity a little bit,'' Brees said, alluding to New Orleans' inability to score more than three points until the first of Michael Thomas' two touchdown catches with 8:41 to go. ''These are games that, hey, you didn't have your best stuff, but you found a way.''
With the help of another Cleveland collapse.
Gonzalez also missed two extra points, one week after his potential winning field goal was blocked in a season-opening tie with Pittsburgh. His final miss came from 52 yards.
''It snowballed,'' Gonzalez said, acknowledging the psychological effect of earlier misses that he hooked left before pushing his final kick the other way. ''I was overcompensating. I get paid to make those kicks and I have to make them.''
Gonzalez's tough day represented only a portion of Cleveland's implosion. Defensive back Derrick Kindred's illegal contact penalty on what would have been a third-down sack extended New Orleans' first touchdown drive, which ended with Thomas' 2-yard catch and cut Cleveland's lead to 12-10.
With just less than five minutes left, Saints safety Marcus Williams intercepted Tyrod Taylor in Cleveland territory on a pass Taylor threw back over the middle as he was rolling to his right.
''You never want to throw late down the middle,'' Taylor said. ''That's something I need to be better at. That play was not good for us. You can't put your team in that situation.''
The turnover led to New Orleans' second TD on a 5-yard fade to Thomas, who said he was determined to make up for his fumble earlier in the game. Thomas outjumped two defenders to make the catch.
''Enough was enough,'' Thomas said. ''I needed to respond and help my teammates, and that's what I did. And I still owe them.''
Brees finished 28 for 35 for 243 yards and two TDs for New Orleans (1-1). Thomas caught 12 passes for 89 yards.
It wasn't enough for the Browns (0-1-1), who were very close to starting 2-0.
''It's tough, but we got a lot of football left to play,'' Landry said.
Alvin Kamara, the 2017 offensive rookie of the year, continued to be a bright spot in a largely frustrating day for New Orleans' offense. His seemingly slippery running style continued to produce yards after contact and he wound up with 99 yards from scrimmage, including 53 on six catches.
His run for a late 2-point conversion gave the Saints an 18-12 lead and made a difference after Taylor found rookie receiver Antonio Callaway for a 47-yard, all-or-nothing TD heave on fourth-and-5 with 1:16 to go.
Gonzalez missed a point-after kick for the second time, and Brees' 42-yard completion to Ted Ginn Jr. set up Lutz' go-ahead kick.
The Browns, who forced six turnovers against Pittsburgh in Week 1, recovered two more fumbles when Thomas and Ginn were both stripped after receptions.
Browns defensive tackle Larry Ogunjobi sacked Brees twice and would have had a third if not for Kindred's penalty.
Overall, it was a strong showing for the unit coached by coordinator Gregg Williams, who held the same job in New Orleans when the Saints won their only Super Bowl.
Browns: Safety Damarious Randall received treatment on the field after being in on a tackle in the second quarter.
Saints: Tommylee Lewis received treatment for what the club described as a knee injury after a big hit during a punt return in the second quarter. He was listed as questionable to return to the game. ... Defensive tackle Sheldon Rankins left in the fourth quarter after taking a hit to the head. He said after the game his face mask was pushed into his nose but that he did not have a concussion.
Browns: Host the New York Jets on Thursday night.
Saints: Visit Atlanta on Sunday.
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