Brady threw for 350 yards and three touchdowns before Vinatieri kicked a 29-yard field goal with 17 seconds left to lead injury-plagued New England past the Atlanta Falcons 31-28 on Sunday.
The Patriots (3-2) avoided their first losing streak since 2002 despite blowing leads of 14-0 and 28-13 to a team that didn't have Michael Vick.
"We put a lot into this one," said Brady, who spouted off in defense of his teammates after a 41-17 loss to San Diego last week. "We've had doubters for a long time. We're just going to keep coming out and doing the hard things every week."
Matt Schaub filled in admirably for the injured Vick, matching Brady's three TD passes, including a tying score with 3:52 remaining. Schaub threw a 14-yard TD to Dez White and then went to Brian Finneran for a two-point conversion.
The Falcons (3-2) had all the momentum, but Brady wasn't concerned.
"We came into a tough environment against an excellent team and had a chance to win the game with three minutes left," he said. "I would take that any day of the week."
With Patriots backed up at their 26 on second-and-20, Atlanta cornerback Allen Rossum was called for a blatant pass interference on Deion Branch -- the last of a four-penalties-in-four-plays stretch that gave New England a first down at the Falcons' 44.
"The offense did a good job in the two-minute drill to get down there and use up all the clock," Vinatieri said. "We found a way to get it done. We've had some ups and downs this year, but this team has a lot of heart."
Vick went out the previous week with a strained ligament in his right knee. In a questionable use of the NFL injury report, he barely practiced all week but was listed as probable until Saturday, when the Falcons downgraded him to questionable.
On Sunday, Vick wasn't active, watching from the sideline, dressed out in a visor and gray sweatshirt.
"He wasn't ready to play," coach Jim Mora said. "It was an easy decision. When a player is not ready to play, you are not going to put him out there in harm's way. This team felt confident we could perform with Matt Schaub, and I think we proved that to be true."
Schaub, a second-year player from Virginia, completed 18-of-34 for 298 yards and didn't have any turnovers. Finneran caught five passes for 103 yards.
"I'm happy with the way I performed," Schaub said. "I thought I came out and made some good decisions and gave us a chance."
But the Falcons' defense couldn't slow Brady, who completed 22-of-27 to lead a 483-yard performance by the Patriots.
"He certainly was making some incredible passes today," defensive end Patrick Kerney said. "When you hit a guy square on his shirt and he's still hitting the receiver, it's frustrating."
Branch, MVP of the last Super Bowl, had eight catches for 107 yards. Tight end Daniel Graham piled up 119 yards on five receptions, including a 45-yard TD. Bethel Johnson hauled in a 55-yard touchdown catch, and Ben Watson went 33 yards with Brady's other scoring play.
Dillon rushed for 106 yards before he went to the locker room with an undisclosed injury late in the game, though he returned to watch Vinatieri's winning kick and wouldn't disclose the nature of his problem.
Pass had the first TD rushing of his career in the opening period.
The Falcons were hurt by potentially season-ending injuries to linebacker Edgerton Hartwell (Achilles tendon) and cornerback Chris Cash (arm). Also, Kerney was limited to passing situations after hurting his oblique (side).
Of course, the Patriots aren't sympathetic about injuries. They lost safety Rodney Harrison for the season and had 14 players on their injury report, including defensive end Richard Seymour, who didn't play.
Graham scored on a brilliant play, taking a simple screen for a long TD. Stephen Neal put a crushing block on Falcons linebacker Demorrio Williams, and then Graham bounced off Bryan Scott and dived into the end zone.
But Atlanta pulled to 14-13 at halftime with two field goals in the final 1:25. The first was expected, Todd Peterson punching through a 33-yarder.
Then, rookie punter Michael Koenen came out with six seconds left to try a 58-yarder, far beyond Peterson's range. The first was wide right, but New England called timeout to give Koenen another try.
This one went through with plenty to spare for the first field goal of his career and second-longest in Falcons history.
Pass rushed for 34 yards on six carries in relief of Dillon. ... The Patriots' last losing streak -- a 24-7 defeat at Tennessee on Dec. 16, 2002, followed a week later by a 30-17 setback at home to the Jets. ... Morten Andersen has the longest field goal in Atlanta history, a 59-yarder in 1995.
The Cardinals quarterback, who had his best NFL season, finished tied for second in MVP voting and came in second for comeback player of the year.
Recapping Saturday's top stories, which include Brett Favre and Ken Stabler headlining the Pro Football Hall of Fame's eight-member 2016 class and the Panthers QB nabbing all but two MVP votes.
Kansas City cornerback Eric Berry, 27, not only beat cancer but played well enough to be recognized for it at the NFL's annual awards show.
Aaron Rodgers' 61-yard, game-winning TD pass to Richard Rodgers vs. the Lions wins the NFL Play of the Year award.
Conan O'Brien, hosting the NFL Honors, worked both Bills coach Rex Ryan and twin brother Rob into bits during the league's annual awards show.
If Johnny Manziel wants help, the NFL and its players are ready to step in, according to NFL executive vice president of football operation Troy Vincent.