The veteran running back ran for just 61 yards, but he came through with a big one at the end.
"I am old, but I can still play," the 33-year-old Jackson said.
The Bears had just punted to open the extra period and Buffalo took over on its own 22 to start the winning possession. The Bills got the ball to the Chicago 39 when the 33-year-old Jackson turned toward the left side and broke off his big run, pushing safety Chris Conte out of the way twice inside the 10 before being knocked out of bounds at the 1.
Buffalo's EJ Manuel backed up 3 yards and put the ball in the middle of the field. After a delay of game, Carpenter won it with a 27-yarder.
Jackson said, "It was a great statement win for us to put all that stuff behind and focus on the season."
The Bears trailed 17-7 at the half after Buffalo scored 17 unanswered points and came up short down the stretch after tying it.
"You guys are going to be as negative as possible," a surly Cutler said. "But we've got a lot of games left, we did a lot of good things. Obviously we made mistakes today and we've got to clean them up and got to keep it going."
Manuel completed 16 of 22 passes for 173 yards for Buffalo. He also had a 2-yard touchdown run in the first quarter.
It wasn't a great afternoon for a revamped defense, either. Allen, the star addition in the offseason overhaul, was a nonfactor in his Bears debut. But Trestman thought it was a good day overall for that group - Jackson's long run aside.
"At the end of the day you keep them in the 17 to 20-point range, that should be enough for us to win," he said. "And if we hang onto the football, take care of it we would have been in a good position to do that."
NOTES: Bills LB Keith Rivers left the game because of a groin injury and S Aaron Williams was being evaluated for a concussion afterward. Buffalo also held out CB Stephon Gilmore because of a nagging groin injury. ... Trestman thought Jeffery might return at some point in the second half, but that didn't happen. ... Slauson and Garza did not think they were seriously injured.
Copyright 2014 by The Associated Press