After holding the Chargers on the first possession of overtime, the Patriots received a huge pass interference call to help set up the game-winning kick.
It was the third field goal of the day for Vinatieri, who also had an extra point blocked.
"The guys out front did a great job blocking," he said. "I'm just the last leg of it. It was an emotional game. We're happy to get the win."
Without a running game, backup quarterback Tom Brady completed 30 of 49 passes for 351 yards, helping the Patriots (2-3) rally from a 10-point, fourth-quarter deficit en route to their second straight home win.
"That shows a Patriot team that is fighting, fighting and fighting," said Brady, who started his third straight game in place of the injured Drew Bledsoe.
New England used to be home to Flutie, a Massachusetts native and former Heisman Trophy winner from Boston College. Flutie, who played briefly for the Patriots in the 1980s, was 20 of 32 for 272 yards, but fell to 12-2 lifetime at Foxboro Stadium.
"It's fun," said Flutie, who gave away 50 tickets to the game. "The people were great and very supportive. It's a fun atmosphere for me to come back to. I just wish we had won."
While Flutie returned home, Terry Glenn returned to New England's lineup and had eight catches for 120 yards and a touchdown. He had six receptions for 97 yards in the first half.
Glenn, a former first-round pick who has had a stormy run in New England, was suspended the first four games of the season for violating the NFL's substance-abuse policy. He also was banned by the team for failing to report to training camp, but had the suspension lifted by an arbitrator.
"I knew I did a lot of things at home to prepare for this big game," said Glenn. "I had high expectations to come out here and contribute. I was mentally thinking that I was going to contribute to this win."
Rookie LaDainian Tomlinson had 73 yards and a touchdown on 24 carries for the Chargers (3-2), who blew a 10-point lead in the final 4 1/2 minutes en route to their second straight loss.
"That's ridiculous," said Flutie, who joined a 1-15 team in the offseason. "They moved the ball and we didn't get first downs. We can't let the ball get back in their hands in that situation. That's where we lost the game."
San Diego appeared to be in control late in regulation as backup fullback Derrick Harris forced punter Norm Johnson into a fumble and returned the ball six yards for a touchdown and a 26-16 lead.
But Brady led a 15-play, 69-yard drive that Vinatieri capped with a 23-yard chip shot as New England cut its deficit to 26-19.
With a chance to run out the clock on their next possession, the Chargers went three-and-out as linebacker Bryan Cox stuffed Tomlinson on third and one.
Troy Brown returned the ensuing punt 40 yards to midfield before Brady went to work.
Brady conneted on passes of 12 and 16 yards to Brown, the second of which came on a third and 10, and threw a 26-yarder to Patten as the Patriots got to San Diego's third.
Without a bona fide running back, the Patriots opted for a play-action pass on the next snap and Brady found wide-open tight end Jermaine Wiggins in the back right corner of the end zone.
The extra point by Vinatieri tied it at 26-26 with 36 seconds left. Each team had previously failed on an extra-point attempt.
"It's really a terrific win for our football team," Pats coach Bill Belichick said. "The players showed a lot of courage coming back down by 10 points with eight minutes to go in the game."
Flutie nearly drove the Chargers into field goal territory on the final possession of regulation as Wade Richey missed a 59-yarder at the gun.
San Diego had the first touch in the extra period and started at its own 39 after a fine kick return by Ronney Jenkins. But the Chargers again went three-and-out before punting away to the Patriots.
New England started from its own 23, but advanced the ball 37 yards when cornerback Alex Molden was called for interfering with Patten after a slight bump down the right sideline.
"I can honestly say that was one of the best experiences in a game I've had," said Patten, who had seven catches for 73 yards. "It was big. That was just as big as a catch. It doesn't go down in the stats but it put us in field goal range."
Brady later kept the drive alive with a nine-yard pass to running back Kevin Faulk on third and five to the Chargers' 26, setting the scene for Vinatieri.
Brady had a career game, finding nine different receivers. Brown led all of them with 11 catches for 117 yards.
Brady was an unlikely hero, especially after passing for a paltry 86 yards in last week's 30-10 loss at Miami.
"I can't say enough about Brady," Belichick said. "We went into the game really wanting to throw the ball, feeling like they have one of the toughest run defenses in the league.
"I'm sure there were some people who didn't think we could do that. But it's really a credit to our players and their attitude and their determination the way they played the last 25 minutes of the game."