LeSean McCoy had a ball stripped from his hands after catching it in the end zone. Leodis McKelvin lost a fumble on a punt return, leading to a Patriots field goal.
And James White eluded safety Corey Graham after making a catch on the right sideline and scored on a 20-yard connection with Tom Brady.
"When we needed plays, we didn't make them," McCoy said after the Bills' 20-13 loss on Monday night. "Against that team, you don't get that many opportunities."
Buffalo's winning streak ended at two games, while the Patriots' winning streak reached 13 dating to last year's postseason.
"The difference is they made some big plays," Bills coach Rex Ryan said. "We came up short many times."
Buffalo (5-5) trails New England (10-0) in the AFC East by five games with six to play and hurt its chances for a wild card.
"We beat ourselves," wide receiver Robert Woods said, "We let this good team off the hook."
Brady completed 20 of 39 passes for 277 yards, hitting White for the running back's first career touchdown late in the second quarter. White added a 6-yard TD run in the third that put the Patriots ahead for good.
McCoy ran 20 times for 82 yards and a 27-yard touchdown and caught six passes for 41 yards to surpass 100 yards from scrimmage for the fourth straight game. The Bills lost to Brady for the 25th time in 28 games.
The game was filled with mistakes, penalties, injuries and turnovers — including two fumbles on a single punt, a rare missed field goal by Stephen Gostkowski and an inadvertent whistle that led to one of many lengthy conferences among the officials.
And New England lost another key player: Danny Amendola, who took over as the Patriots' No. 1 receiver because of last week's injury to Julian Edelman, caught nine passes for 117 yards before leaving with a knee injury of his own in the third quarter.
With the wind chill temperature at 21 degrees at kickoff, both teams struggled on offense, and the Patriots even failed to score in the fourth — the first time they were shut out in a quarter since the first one of the season.
In the third quarter, both teams fumbled on the same punt.
McKelvin fielded a punt at his own 30 and made it just 2 yards before the ball was knocked out by Brandon King. New England's Jonathan Freeny picked up the ball and rumbled 5 yards before he lost the ball and it bounced out of bounds.
The Patriots took over at the Buffalo 30 and took a 20-10 lead on Gostkowski's 35-yard field goal.
Even the referees were sloppy.
Early in the third, Brady rolled toward the right sideline before throwing downfield to Amendola. As the receiver broke for the end zone, the play was whistled dead — apparently because the official thought Brady stepped out of bounds.
After a lengthy discussion, the referee announced there was an inadvertent whistle. The 14-yard reception counted, with a 15-yard penalty for interference from the Bills coaching staff. The drive ended with an even more unusual error: Gostkowski's first miss in 51 weeks.
Brady threw a first-half interception that was nullified by offsetting penalties. But he did throw one at the Buffalo goal line in the fourth that stuck.
Brady took a dig at Ryan in the first quarter by adding "Rex Ryan!" to his pre-snap signals. The Bills coach has been a longtime rival of the Patriots.
But the Patriots managed just a field goal in the first, and then went scoreless for 22 minutes, 16 seconds before Brady led a 33-second touchdown drive to make it 10-3 with 13 seconds left in the half.
Brady threw an out pass to White, who broke a tackle along the sideline to score from 20 yards out.
That prolonged New England's scoring streak, but it came to an end at 38 in a row when they failed to score in the fourth.
And another streak was snapped, too.
Gostkowski hadn't missed a kick all season, a total of 22 field goals and 35 extra points before his attempt from 54 yards out in the third quarter sailed wide right. It was his first miss since Nov. 30, 2014, and his first miss at home since Week 2 of the 2013 season.
NOTES: McCoy is the first Buffalo player to rush for more than 100 yards in four consecutive games since C.J. Spiller in 2012. ... Patriots injuries: Amendola (knee) and WR Aaron Dobson (ankle). Bills injuries: WR Marcus Easley (head), OL John Miller (ankle), S Bacarri Rambo (shoulder), DL Mario Williams (foot), TE Charles Clay (neck).