The reigning NFL Most Valuable Player completed 19-of-30 passes and ran six times for 40 yards as Buffalo improved to 7-3, 1.5 games behind NFL-best New England (9-2) in the AFC East division.
Allen became the only player in NFL history with multiple games of three rushing and passing touchdowns.
"I'm doing my job," Allen said. "Things weren't going the way we wanted, (we were) just trying to find a way to reset. (I) trusted my feet and finding completions, we did that better in the second half."
Allen scored on a two-yard run in the first quarter and threw scoring passes of 43 yards to Tyrell Shavers, 52 yards to Ty Johnson and 25 yards to James Cook, but the Buccaneers led the Bills 32-31 with 13:38 remaining.
Undaunted, Allen drove the Bills 81 yards in eight plays to score on a five-yard run and added a nine-yard touchdown run with 2:35 remaining off an 85-yard march to secure Buffalo's victory.
"(We) turned the ball over three times and somehow found a way to win the way we did, that speaks a lot to the resiliency we have in this locker room," Allen said.
"We're going to try to use this momentum going forward."
Sean Tucker ran for 106 yards and two touchdowns for Tampa Bay (6-4).
The Denver Broncos edged Kansas City 22-19 for their eighth NFL triumph in a row. Denver's Wil Lutz kicked his fifth field goal, a 35-yarder on the final play, as the Broncos improved to 6-0 at home and the Chiefs fell to 5-5.
"It was huge," Denver quarterback Bo Nix said. "This was a must-win going into a bye week. We knew it was going to be tough."
In a showdown of NFC West co-leaders, Matthew Stafford threw for two touchdowns and the Los Angeles Rams intercepted four passes by Seattle's Sam Darnold in a 21-19 Rams home victory.
Final play field goals
Carolina (6-5) moved within a half-game of the Bucs in the NFC South, with a 30-27 overtime victory in Atlanta. Bryce Young threw for 448 yards and three touchdowns while Ryan Fitzgerald kicked a 28-yard field goal on the final play to win for the Panthers.
Carlos Santos kicked a 48-yard field goal on the final play to give Chicago a 19-17 victory at Minnesota, keeping the Bears atop the NFC North.
Pittsburgh got a 73-yard interception return touchdown from Kyle Dugger and a 34-yard fumble recovery touchdown from James Pierre in a 34-12 rout of visiting Cincinnati.
The Steelers, however, lost 41-year-old quarterback Aaron Rodgers to a left wrist injury in the second quarter.
Pittsburgh safety Jalen Ramsey was ejected for throwing a punch at Cincinnati receiver Ja'Marr Chase after video appeared to show Chase spitting at Ramsey.
Rodgers' replacement in Green Bay, Jordan Love, threw for 174 yards and two touchdowns, including the game-winner on a 17-yard touchdown pass to Christian Watson with 4:02 remaining, as Green Bay won 27-20 at the New York Giants.
For Jacksonville, Trevor Lawrence threw for one touchdown and ran for another while Travis Etienne ran for two touchdowns in a 35-6 rout of the visiting Los Angeles Chargers.
Matthew Wright's 35-yard field goal on the final play gave Houston a 16-13 triumph at Tennessee.
At cold and windy Philadelphia, the reigning NFL champion Eagles outlasted Detroit 16-9 as Jalen Hurts threw for 135 yards and ran for 31 yards and a touchdown.
Miami down Washington in Madrid
In Madrid, Jack Jones intercepted a Marcus Mariota pass to set up Riley Patterson's 29-yard field goal in overtime that lifted Miami over Washington 16-13 in the NFL's first regular-season game in Spain.
"It has been a great experience being out here. It was a great game for them to come out here and experience," said Miami's De'Von Achane, who had 21 carries for 120 yards and five catches for 45 yards.
Brock Purdy threw for 200 yards and three touchdowns and Christian McCaffrey ran for 81 yards and two touchdowns in San Francisco's 41-22 victory at Arizona. Cardinals quarterback Jacoby Brissett broke the record for the most completions in an NFL game with 47 from 57 attempts.
Matthew Wright's 35-yard field goal on the final play gave Houston a 16-13 triumph at Tennessee.
Baltimore tight end Mark Andrews ran 35 yards for the winning touchdown with 2:31 remaining in the Ravens' 23-16 victory at Cleveland.
Shedeur Sanders, son of retired legend Deon Sanders, made his NFL debut for Cleveland after rookie quarterback Dillon Gabriel was sidelined by a concussion, but couldn't rally the Browns for a comeback triumph.