Jackson ran for just 61 yards, but he came through with a big one at the end.
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 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 2 yards and put the ball in the middle of the field. After a delay of game, Carpenter won it with a 27-yarder.
It was a good start for the Bills as they enter a new era following the death of founding father and Hall of Fame owner Ralph Wilson. They're trying to end a 14-year playoff drought and they started by knocking off a team eyeing a run to the postseason.
Bills offensive lineman Eric Wood took to Twitter after the game, apologizing to fans who may have doubted the Bills.
Great team win! Sorry about all your survivor pools out there - Eric Wood (@EWood70) September 7, 2014
This was not what the Bears had in mind. They got little pressure from a revamped defense despite the addition of five-time Pro Bowl end Jared Allen, and there were some questionable decisions at times by Jay Cutler, who got picked off twice while throwing for 349 yards and two touchdowns.
The Bears trailed 17-7 at the half after Buffalo scored 17 unanswered points and came up short down the stretch after tying it.
The Bills looked like they might pull this one out in regulation with a 20-17 lead after Dan Carpenter kicked a 33-yard field goal.
But the Bears answered after the Bills grabbed the lead.
They drove from the 20 to the Buffalo 19, and Cutler threw an incomplete pass to Brandon Marshall in the end zone before Robbie Gould tied it with a 37-yard field goal with 30 seconds left in regulation.
Manuel completed 16 of 22 passes for 173 yards for Buffalo. He also had a 2-yard touchdown run in the first quarter.
Robert Woods added 78 yards receiving.
Chicago's Matt Forte ran for 82 yards and had 87 receiving. Brandon Marshall and Alshon Jeffery each added 71 yards receiving, although Jeffery was limited by a hamstring injury. Marshall had a TD catch.
Information from The Associated Press was used in this report.