Allen achieved the unique feat of throwing, catching and rushing for a touchdown in the same game - according to NFL.com, he became the first quarterback to score in all three ways in a league game.
The play of the game came in the third quarter when Allen threw a short pass to Amari Cooper, who threw it back to him and Allen caught the ball before rushing into the end zone to make it 28-3.
"I threw a bad ball. I was worried it was going to get tipped up in the air and picked, so I was just kind of chasing it," said Allen.
"I made eye contact with Coop. He's a vet. Saw me, I put my hands out, he tossed it to me, and I had to make a play," he said, before noting the fantasy football points significance of him being credited a touchdown pass and catch on the same play.
Earlier, James Cook had scored an equally spectacular but more orthodox touchdown when he rushed 65 yards over the snow-covered field mid-way through the second to make it 14-3.
Allen followed up that score with a seven-yard pass to Mack Hollins, finished off the rout by rushing in himself for an eight-yard score as the impressive Bills moved to 10-2 and clinched the AFC East division crown and a play-off berth.
Pittsburgh quarterback Russell Wilson continued his renaissance, throwing for 414 yards and three touchdowns as the Steelers won 44-38 at the Cincinnati Bengals.
Wilson, a Super Bowl winner with Seattle in 2014, was released by Denver last year and signed a one-year veteran minimum deal with the Steelers. But having earned the starting role in Pittsburgh, ahead of Justin Fields, the veteran is spearheading the team's strong push towards the playoffs.
Wilson's 25-yard touchdown pass to Pat Freiermuth at the end of the third quarter was a reminder of his enduring quality, scrambling out of the pocket and finding his receiver with a fine pass on the run.
That score gave the Steelers a 34-24 lead heading into the fourth, and a 21-yard fumble recovery returned by Payton Wilson put them in firm control.
Although Bengals quarterback Joe Burrow threw two touchdowns in the final quarter, either side of a 30-yard Chris Boswell field goal for the Steelers, the Steelers held on for a crucial win against their divisional rivals.
The Steelers lead the AFC North on 9-3 with the Baltimore Ravens second on 8-4.
Vikings vs. Cardinals
Sam Darnold threw a game-winning touchdown in the final minutes as the Minnesota Vikings fought back to beat the Arizona Cardinals 23-22 for their fifth straight win.
The Vikings sit on 10-2 for the season but are in second place in the highly competitive NFC North which is led by the 11-1 Detroit Lions with the Green Bay Packers on 9-3.
The Vikings trailed 22-16 with 1:13 left when Darnold found Aaron Jones to his right and the running back dashed into the end-zone for a 5-yard score.
It was the first time that the Vikings had been ahead in the game, in which Darnold threw for 235 yards and two touchdowns.
Around the league
Geno Smith returned to haunt the New York Jets as he led the Seahawks to a 26-21 victory, clinched by Zach Charbonnet's 8-yard rushing score in the fourth.
The former Jets quarterback threw for 206 yards and a touchdown while opposite number Aaron Rodgers threw for 185 yards and two touchdowns.
Jayden Daniels threw three touchdowns and ran in another as the Washington Commanders crushed the Tennessee Titans 42-19.
The Los Angeles Chargers (8-4) handed Atlanta their third straight loss with a 17-13 win with Falcons quarterback Kirk Cousins throwing four interceptions.
The Indianapolis Colts beat the New England Patriots 25-24 with Anthony Richardson throwing a three-yard touchdown pass to Alec Pierce with 12 seconds left before the quarterback ran in the game-winning 2-point conversion.