Tyler Bass atoned for a miss by kicking a 22-yard field goal that put the Bills ahead with 3:43 remaining and Buffalo held on to end a two-game skid, improving to 4-2 to tighten their grip on the NFL's AFC East division.
The Jets dropped to 2-4, third behind the Bills and Miami Dolphins with the 1-5 New England Patriots in last place.
"We found a way to win," Allen told broadcaster ESPN. "Got sloppy in the second half, got to find a way to put more points on the board, but it was a team victory. We'll take 'em how we get 'em."
The Jets suffered their third straight defeat, and their first since sacking head coach Robert Saleh on Tuesday.
Defensive coordinator Jeff Ulbrich was installed as interim coach in the shake-up, which saw offensive coordinator Nathanial Hackett relieved of play-calling duties.
But there was no change in the outcome, despite an impressive 294 passing yards for Rodgers with two touchdowns and an interception.
Rodgers ended the first half with a spectacular Hail Mary pass that Allen Lazard reeled in for a 52-yard touchdown that pulled the Jets within 20-17 at halftime.
Greg Zuerlein booted a 22-yard field goal to make it 20-20 in the third quarter. But Zuerlein missed go-ahead field goal attempts of 32 and 43 yards off the left upright in the second half.
Those were just two of the Jets' missed opportunities.
With less than two minutes remaining, Rodgers threw a long pass intended for Mike Williams but the throw was short and Taron Johnson -- back after breaking his right arm in the season opener -- grabbed the interception.
Allen and the Bills were able to run out the clock and seal the victory in a game that saw both teams assessed 11 penalties for a total of 204 yards.
After the Jets scored a field goal on their opening drive, the Bills answered with a drive capped by Allen's one-yard TD run.
Rodgers connected with Garrett Wilson with a five-yard scoring pass to make it 10-7 after one quarter, but Allen came up with an eight-yard TD pass to Mack Hollins and a 12-yarder to Dawson Knox late in the second quarter to put the Bills in front.
