In freezing conditions at Buffalo's Highmark Stadium, Bills quarterback Allen threw three touchdowns and conjured a scintillating 52-yard run for a superb rushing touchdown to help take down the seventh-seeded Steelers.
The victory sends the Bills into another play-off clash with Patrick Mahomes and the Kansas City Chiefs, the reigning Super Bowl champions who head to Buffalo on Sunday for a mouthwatering Divisional Round battle.
Buffalo were beaten in Kansas City in the AFC play-offs in 2022 and 2021, in two classic high-scoring encounters.
"It's going to take a team effort," Allen said of facing the Chiefs.
"We know the type of team that they are, obviously the type of quarterback that they have in Pat over there."
Allen and the Bills laid the foundation for victory with a devastating first-half display that took full advantage of Pittsburgh's offensive ineptitude.
Monday's game had been shifted from Saturday due to the winter storm that enveloped swathes of the United States last week. While the pitch at Orchard Park was cleared in time for kick-off, thick snow blanketed the stands.
When the game finally got underway, Allen was too hot to handle as the Bills roared into a 21-0 lead.
Allen found Dawson Knox for the opening touchdown to cap an 80-yard drive and then punished a Steelers fumble on the next possession with a 29-yard bullet into the end zone for tight end Dalton Kincaid.
Allen then brought the house down midway through the second quarter with a magical individual score, showcasing the quarterback's athleticism by charging 52 yards for a rushing touchdown that made it 21-0.
At that stage, the Bills looked to be cruising to a blowout victory against a Steelers offence whose first five possessions of the game resulted in three punts, a fumble and an interception.
Eagles crash
Pittsburgh did rally to get within seven points early in the fourth quarter at 24-17, Mason Rudolph marching the Steelers 75 yards upfield before passing to Calvin Austin III for a touchdown.
Yet the Bills responded with their fourth touchdown of the game to restore the 14-point cushion, Khalil Shakir stooping to gather a pass from Allen before jinking into the end zone.
In Monday's NFC Wild-Card game meanwhile, Philadelphia crashed out of the play-offs in the final act of a late-season collapse that saw them go from potential Super Bowl contenders to whipping boys.
At the start of December, the Eagles - narrowly beaten in last year's Super Bowl - were 10-1 and looked a good bet to return to next month's NFL championship game in Las Vegas.
But the Eagles' season unravelled with five defeats in their final regular season six games, and the denouement came in Florida on Monday as Tampa Bay became the latest team to expose their brittleness.
Tampa Bay, who claimed victory in the 2021 Super Bowl with Tom Brady at quarterback, will now head to Detroit on Sunday in the divisional round.
Monday's victory marked a personal triumph for Buccaneers quarterback Baker Mayfield, who threw three touchdowns and no interceptions to finish with 337 passing yards.
Mayfield entered the NFL in 2018 after being chosen by the Cleveland Browns with the No. 1 pick in the Draft.
But the 28-year-old was jettisoned by the Browns in 2022 and struggled to rebuild his career during separate stints with the Carolina Panthers and Los Angeles Rams before joining Tampa Bay in 2023.
On Monday, Mayfield led the Bucs to a 10-0 first-quarter lead, tossing a 44-yard pass to David Moore for Tampa Bay's opening touchdown.
Mayfield then connected with Trey Palmer for a 56-yard touchdown in the third quarter before capping the win in the fourth with a 23-yard completion to Chris Godwin to seal a memorable win.
"We've fought so hard to get in the play-offs to get to this point," Mayfield said afterwards. "We came out and started fast and I'm so proud. We wanted to give ourselves a chance and we did just that.
"We can play better than we did tonight but it's on to the next one. We're on to Detroit."
