After spiking the ball, Gronkowski spun and took a bow.
The Bills (4-4) sputtered minus their offensive top threat, running back LeSean McCoy, who has a hamstring injury. And their defense was unable to keep the Patriots in check despite star defensive tackle Marcell Dareus making his season debut.
Of his 20 regular-season games with four touchdowns passing or more, six have been against Buffalo.
The Patriots punted just three times and converted nine of 13 third-down opportunities.
The Patriots then broke the game open by scoring 27 points over five consecutive possessions in a surge that began with Gronkowski scoring his 69th career touchdown to break a franchise record previously held by Stanley Morgan.
Patriots: Amendola's 73-yard kickoff return to open the second half led to Brady's 12-yard TD pass to Edelman to put New England up 31-10.

Patriots: None reported.
GRONK MILESTONE
Dareus missed the past three games because a hamstring injury, and missed the start of the season serving a four-game suspension for violating the NFL's substance abuse policy.
Brady went 22 of 33 for 315 yards and threw four touchdowns in leading New England to a 41-25 win. He improved to 26-3 against Buffalo , matching a record set by Brett Favre,Nike Air Max 95 Cheap, who went 26-9 against Detroit.
"We've had a lot of experiences where there's 70,000 people against you," Brady said. "And at the end there's 5,000 Patriots (fans) on the road that are cheering for us. ... To be so far ahead you can run out the clock, it's a great feeling."
He said he bowed in tribute to his mother, Diane, who met with Gronkowski at the team hotel on Saturday and told him how proud she would be for him to break the record.
Best of all,Cheap Jerseys, Brady's performance had Bills fans heading for the exits early in the fourth quarter, what whatever Patriots fans remained as the clock wound down.
"I was like, I've got to give her a shoutout for letting me know she's super proud of me," he said. "Hi mom and thank you."
"Obviously, we weren't good enough," Bills coach Rex Ryan said. "We made way too many mistakes, mistakes that we haven't made all season. And against a guy like Brady, he makes you pay."
"You know, they like to talk all that. They got that win," said tight end Rob Gronkowski, who had 109 yards receiving and a touchdown. "I'm so glad we came in here and showed them what we're really about."
Bills: LB Lorenzo Alexander did not return after hurting one of his hamstrings during a punt return in the second quarter. Receiver Brandon Tate (concussion protocol) did not return after being tackled by Devin McCourty in the third quarter. RB Reggie Bush hurt his groin,Cheap Jerseys From China.
Danny Amendola and Julian Edelman also caught touchdown passes, while LeGarrette Blount scored on a 1-yard run.
INJURIES
Bills: Bills punter Colton Schmidt bumbled his drop while facing fourth-and-15 at his own 20. He quickly scooped it up and broke up the right sideline for a 16-yard gain. Buffalo eventually went on to score on Taylor's 26-yard run to cut the Patriots lead to 31-17 midway through the third quarter.
For Brady, it was his first four-TD outing since a 36-7 win over Miami last October. It was the most he's had on the road since throwing four in a 37-22 win at Orchard Park on Oct. 12, 2014.
Backup running back Mike Gillislee scored on a 3-yard run and Taylor scrambled for a 26-yard touchdown on fourth down in the third quarter. Jonathan Williams scored on a 1-yard run with 30 seconds left.
SPECIAL TEAMS
After a Bills field goal, Brady threw touchdowns passes on his first two drives. They included a 53-yarder to former Bills receiver Chris Hogan , who beat cornerback Stephon Gilmore up the left sideline.
The Patriots (7-1) have won four straight since Brady returned after opening the season serving the NFL's four-game "Deflategate" suspension. His absence included New England's only blemish, a 16-0 home loss to Buffalo on Oct.  2,Wholesale Jerseys NFL, the first time the Patriots were shut out at home since 1993.
SACK ATTACK
ORCHARD PARK, N.Y. (AP) — Patriots quarterback Tom Brady asserted his on-field ownership of the Buffalo Bills again Sunday, matching an NFL record in beating them for the 26th time.
The Bills had five sacks, upping their season total to 26 — five more than they managed all last season. Veteran defensive tackle Kyle Williams had one, his 38th, moving into eighth on the franchise list, one ahead of Sherman White.