Brady (294) also moved ahead of Warren Moon into sole possession of sixth place for most touchdown passes in NFL history and reached the 4,000-yard mark for the fourth time in his career. Gronkowski caught six passes for 160 yards.
Rex Grossman was 19 of 32 for 252 yards, and Roy Helu (126 yards) became the first Washington rookie to run for 100 yards in three straight games. But it wasn't enough for the Redskins (4-9), who have lost eight of nine.
With the Patriots leading by seven in the fourth quarter, Brady had a chance to extend the lead, but he was picked off in the end zone by Josh Wilson with 6:30 to play. Afterward, Brady was involved in a heated exchange on the sideline with an assistant coach.
The Redskins took advantage of the miscue, driving from their own 20 to the New England. But Santana Moss' catch at the goal line was negated by a pass interference call on the receiver, and then Moss tipped a pass into the hands of Mayo to save the day for a New England defense that ranks last in the league in yards allowed.
There was lots of scoring, and nearly every drive had a highlight.
Already playing without tight end Fred Davis and left tackle Trent Williams both suspended for the rest of the season last week for violating the NFL's substance abuse policy the Redskins lost another offensive starter during pregame warm-ups when right tackle Jammal Brown injured his right groin.
So, with Washington starting its sixth different starting offensive line in nine weeks, it was almost predictable that Grossman would hold the ball too long in the end zone while undrafted rookie left tackle Willie Smith was getting beat by ex-Redskins defensive end Andre Carter. Carter jarred the ball loose, getting his 10th sack of the season, and Vince Wilfork recovered for a touchdown to put the Patriots ahead before the game was three minutes old.
After that, it was mostly offense, and Gronkowski had the best highlights in a series that lasted all of two plays: one remarkable, one record-setting.
On the first, he made a diving catch, got up, dragged DeJon Gomes and Reed Doughty a few yards and escaped while tiptoeing along the sidelines as cornerback DeAngelo Hall stood and watched. Gronkowski tiptoed again when hit by Wilson and stumbled ahead before falling to complete the 49-yard gain.
On the next play, Gronkowski was open to catch Brady's 11-yard pass, his 14th touchdown reception of the season, passing Antonio Gates (2004) and Vernon Davis (2009). Gronkowski unleashed an almighty spike and retrieved the ball for safekeeping, just as he did last week when he thought he had set the record, only to realize that the play had been scored as a lateral instead of a pass.
Washington's Jabar Gaffney was a bit overenthusiastic while celebrating the game's next touchdown, a 9-yard catch. He leaped into the first row of stands but no one caught him and he sank behind the barrier.
The next score came on the first offensive play of the year for Redskins kick returner Brandon Banks, who took a pitch on a double reverse and flung his first career pass 49-yards to Moss give Washington a 17-14 lead.
A couple of curious personal foul calls for hits to the quarterback, one on Carter and one on Washington's London Fletcher, highlighted a pair of field goal drives that left the score tied at 20 at the half. The whistle on Fletcher appeared particularly egregious; the refereed announced that Fletcher hit a late-sliding Brady with a forearm to the head, but Fletcher's arm clearly hit the quarterback in the chest.
The second half continued at the same whiplash speed, with three third-quarter drives going for touchdowns. Gronkowski broke rookie Ryan Kerrigan's attempt at a tackle and padded his record with a 37-yard scoring reception, and David Anderson's first TD catch since 2008 tied the game at 27 on the next drive. Then it was Brady to Wes Welker for 24 yards to restore New England's lead.
Joseph White can be reached at http://twitter.com/JGWhiteAP
New England 34, Washington 27
New England 14 6 14 0 34
Washington 10 10 7 0 27
NE • Wilfork fumble recovery in end zone (Gostkowski kick), 12:06.
Was • FG Gano 24, 6:42.
NE • Gronkowski 11 pass from Brady (Gostkowski kick), 5:49.
Was • Gaffney 9 pass from Grossman (Gano kick), 1:20.
Was • Moss 49 pass from Banks (Gano kick), 14:49.
NE • FG Gostkowski 23, 8:54.
Was • FG Gano 25, 2:13.
NE • FG Gostkowski 24, :00.
NE • Gronkowski 37 pass from Brady (Gostkowski kick), 12:05.
Was • Anderson 6 pass from Grossman (Gano kick), 6:58.
NE • Welker 24 pass from Brady (Gostkowski kick), 4:26.
Attendance • 77,825.
First downs 22 25
Total Net Yards 431 463
Rushes-yards 20-79 34-170
Passing 352 293
Punt Returns 2-18 0-0
Kickoff Returns 2-39 6-117
Interceptions Ret. 1-2 1-0
Comp-Att-Int 22-37-1 20-33-1
Sacked-Yards Lost 1-5 2-8
Punts 3-45.0 3-37.3
Fumbles-Lost 0-0 2-1
Penalties-yards 4-47 8-73
Time of Possession 23:51 36:09
Rushing • New England, Woodhead 8-41, Green-Ellis 5-19, Faulk 3-11, Brady 4-8. Washington, Helu 27-126, Royster 6-44, Grossman 1-0.
Passing • New England, Brady 22-37-1-357. Washington, Grossman 19-32-1-252, Banks 1-1-0-49.
Receiving • New England, Welker 7-86, Gronkowski 6-160, Hernandez 5-84, Ochocinco 1-15, Underwood 1-7, Woodhead 1-4, Faulk 1-1. Washington, Gaffney 6-92, Stallworth 4-96, Moss 3-81, Anderson 2-12, Helu 2-6, Royster 2-6, Young 1-8.
Missed Field Goals • None.