Defensive end Jared Odrick picked off a deflected pass to set up a Miami touchdown and end Brady's NFL-record streak of 358 passes without an interception.
New England totaled 622 yards, the most in franchise history and the most allowed by Miami. Brady's performance overshadowed Miami's Chad Henne, who threw for a career-high 416 yards.
The 906 net yards passing by both teams was an NFL record.
FOXBOROUGH, Mass. (AP) - Tom Brady threw for 423 yards six days after setting a single-game team record of 517 in leading New England.
Brady had three touchdown passes and tied for the third most yards passing in club history, going 31 of 40 with no interceptions as the Patriots scored on each of their four first-half possessions.
ORCHARD PARK, N.Y. (AP) - Rian Lindell hit a 28-yard field goal as time expired and Buffalo snapped a 15-game losing streak against New England and lifted its record to 3-0.
Buffalo was in dramatic fashion, overcoming a 21-0 second-quarter deficit. It was the second straight week the Bills rallied; they overcame a 21-3 deficit in a 38-35 win over Oakland last week.
Ryan Fitzpatrick went 27 of 40 for 369 yards with two TDs as Buffalo beat its AFC East rival for the first time since the 2003 opener. It was the third-longest losing streak against one opponent in NFL history.
OAKLAND, Calif. (AP) - Tom Brady bounced back from a four-interception performance by throwing for 226 yards, two touchdowns and committing no turnovers.
Meanwhile, New York's Mark Sanchez had another tough one, passing for just 166 yards against the team that entered with the NFL's lowest-ranked defense.
Dan Bailey's 26-yard field goal had broken a 13-13 tie with 5:13 left. Each team ran one series before the Patriots got the ball after a punt with 2:30 remaining. Brady then completed eight of nine passes for 78 yards on an 80-play drive capped by his pass to Hernandez in the middle of the end zone.
New England won despite its first two lost fumbles of the season and Brady's two interceptions.
Roethlisberger completed 36 of 50 passes and led the Steelers on a series of clock-chewing drives, effectively keeping Brady and the NFL's top-ranked offense off the field. Pittsburgh held the ball for more than 39 minutes and survived a late rally to win its fourth straight following a 2-2 start.
Brady passed for two touchdowns but threw for a season-low 198 yards and couldn't get into any sort of rhythm while losing to the Steelers for just the second time in his career.
Down 10-0 early, the AFC East-leading Patriots rallied behind Brady. New England scored on five of its next six possessions, excluding a kneel-down at the end of the first half.
FOXBOROUGH, Mass. (AP) - Rob Gronkowski caught two touchdown passes then scored on a lateral and New England then withstood a fourth-quarter rally to keep Indianapolis winless.
The Patriots won another AFC East title by bouncing back from an early 17-6 deficit and an awful first quarter in which they were outgained on the ground 167 yards to 4.
This time, there was no last-minute magic from Tebow, Denver's enigmatic quarterback who had guided the Broncos to four straight fourth-quarter comebacks and six straight wins.
Instead of another slow start followed by a fantastic finish, the Broncos started out fast and then fizzled. They scored on their first three possessions and then were done in by a trio of second-quarter turnovers.
FOXBOROUGH, Mass. (AP) - Tom Brady ran for two touchdowns and threw for another and New England rallied to clinch a playoff bye.
The Patriots (13-3) finished the season with eight straight wins. But for the second straight game, they fell behind early. They beat the Miami Dolphins 27-24 after trailing 17-0 at halftime then rallied after the Bills scored touchdowns on their first three possessions, drawing boos from the home fans.
Brady even punted with 2:56 remaining, 48 yards on third down.
And so ended one of the season's most exciting story lines - one that caught the nation's attention and began when Denver was 1-4 and made Tebow a starter. The one-time third-stringer promptly won six in a row and seven of eight, with a string of stunning comebacks, and the Broncos ended up backing into the AFC West title.
Brady scored the winning touchdown when he leaped over the vaunted Ravens defense in the fourth quarter.