"My priority was to get him in the end zone," the Patriots defensive end said. "We're tied up, so I'm thinking, 'Let me get this dude.'"
Losman went down, the official's arms went up and New England beat the Buffalo Bills 19-17 with poise under pressure and increasing pressure by a defensive line.
"I should have gotten rid of the ball, but the game was on the line," Losman said. "I dipped under one defender, but then there was another guy."
Warren's game-winning safety with 8:33 left completed a comeback from a very poor start that had the Patriots trailing 17-7 at halftime. Even the pregame activities were missing something.
For the first time in three years, the Patriots' season opener was not preceded by the unveiling of a championship banner. Kicker Adam Vinatieri, wide receiver David Givens and linebacker Willie McGinest were elsewhere after leaving as free agents.
"It's no way to start the season, but we recovered and came back and put together a nice drive after that," said Brady, who was disappointed with his performance, 11-for-23 for 163 yards, two touchdowns and an interception.
Bill Belichick became the 31st coach in NFL history with 100 regular-season wins, improving his record to 100-77.
New England cut the lead to 17-14 with 2:52 left in the third quarter on Brady's 17-yard pass to Kevin Faulk after Buffalo went for it on fourth-and-1 at the Patriots' 7-yard line and the line stopped Willis McGahee for no gain.
"That felt great," Patriots nose tackle Vince Wilfork said. "The fans got into it and we got into it."
McGahee wasn't sure what was happening.
"I wasn't worried. I thought it was third down," he said. "It was the play to run."
The pressure was on again when Stephen Gostkowski, the rookie replacing Vinatieri, connected on a 32-yard field goal that tied the game at 17 with 9:33 remaining.
Exactly one minute later, the Patriots took the lead for good on the third play of Buffalo's possession, sending the Bills to their sixth straight loss against New England.
On the first two plays, Losman threw the ball away under a heavy rush and McGahee was thrown for a 1-yard loss.
Then Losman dropped about 4 yards into the end zone as linebacker Tully Banta-Cain rushed from Losman's left and got a hand on the quarterback. Warren, charging in from the other side, tackled Losman for the safety.
"We handled it early, but their pressure mounted as the game went on," Buffalo coach Dick Jauron said.
On the third play of the Bills' next possession, Richard Seymour sacked Losman for a 6-yard loss, Brian Moorman punted and the Patriots held the ball for the remaining 6:15. Losman finished 15-for-23 for 164 yards.
"You can tell why they have won three of the last five Super Bowls," defensive end Aaron Schobel said. "They know how to finish games."
Buffalo, with a new coaching staff, dominated early, starting with the sack by Spikes, who missed the last 13 games last season with a torn Achilles' tendon and left Sunday's game on the Patriots second series with a mild hamstring injury that he doesn't expect to hold him out of next Sunday's game at Miami.
The Patriots tied it 7-7 on their next possession on Brady's 9-yard scoring pass to Troy Brown. Buffalo regained the lead on Rian Lindell's 53-yard field goal and then made it 17-7 on an 18-yard run by Anthony Thomas.
"He runs one way, I run another and we keep fresh legs in the game," Maroney said.
On defense, they were fresh enough to send Losman and the Bills to defeat.
"We're as good as we want to be," Warren said, but " it's too early in the season to be putting crowns on anyone's head."
The Patriots improved their winning percentage to .500 over their 47-year history at 356-356-9. ... Neither team had a receiver with more than three catches -- Josh Reed and Peerless Price for Buffalo and Benjamin Watson for New England. ... Buffalo had 21 players who weren't on last year's team. ... The Patriots converted both of their fourth-down opportunities. The Bills failed on their only one.