The Broncos (4-3) won for the 12th time in their last 13 home meetings with the Patriots (3-4), dating to 1968.
Denver was trailing by 10 points when Griese found Rod Smith for a 65-yard touchdown strike 4:25 into the third quarter, helping the receiver move past Steve Watson into third place on the Broncos' all-time receiving yards list with 6,171.
"The 65-yard touchdown catch by Rod Smith was one of several turning points," Broncos coach Mike Shanahan said. "We needed a shot in the arm and that provided it."
The Pro Bowl quarterback hit tight end Dwayne Carswell with a six-yard touchdown pass to give the Broncos their first lead of the game, 24-20. Griese hit 19 of 30 passes for 283 yards after struggling in his last two games with a recurring shoulder problem.
Walker recorded his second interception of the game and ran untouched into the end zone with 2:24 left as the Broncos snapped their two-game losing streak.
In the duel of Michigan quarterbacks, Tom Brady threw four interceptions on New England's final four possessions after not recording one in his 134 career attempts entering Sunday. He completed 25 of 38 passes for 203 yards and two touchdowns, but slipped to 3-2 as the Patriots' starter since they lost Drew Bledsoe to a chest injury.
Brady was the backup to Griese when the Wolverines won the national championship in 1997.
The AFC's top two receivers had outstanding games. Smith had six catches for 159 yards to record his 25th career 100-yard game. New England's Troy Brown registered nine receptions for 86 yards and a touchdown.
Denver opened up its passing game after New England's Adam Vinatieri kicked a 44-yard field goal 4:01 into the third quarter, giving the Patriots a 20-10 cushion.
On the first play from scrimmage after the ensuing kickoff, Griese found Smith in stride as the Broncos began their comeback.
"I think it's a credit to him, to what kind of day he had after being double-covered," Griese said of Smith.
"Both Otis Smith and Matt Stevens made a big mistake on the play," Patriots coach Bill Belichick said. "Those are the kind of plays that really cost us the game. You've got a receiver doubled and he catches a 65-yard touchdown pass."
Denver took the lead on its next possession. Griese completed a 35-yard pass to tight end Desmond Clark on third and two and a 21-yarder to Smith as the Broncos advanced to the Patroits' 19.
"They played a lot of eight-man front and so we took advantage of it and threw the ball down field," Shanahan said. "For the most part they took our running game away. Brian threw the ball well today."
Olandis Gary picked up 13 yards on two carries before Griese connected with Carswell on the ninth play of an 80-yard drive for the go-ahead score.
Mike Anderson and Gary, who each have recorded a 1,000-yard season, combined to gain 77 yards on 24 carries.
Former league MVP Terrell Davis did not play, despite returning to practice for the Broncos this week. The running back had his right knee surgically repaired five weeks ago.
In the first three quarters, Brady continued his outstanding play, completing 21 of 24 passes for 163 yards and two touchdowns. But he looked like a backup over the final 15 minutes, throwing for only 40 yards to go along with his four interceptions.
"We just made too many mistakes today," Brady said. "In the first half we played our type of game. But after halftime, our communication was not the best."
With a pass intended for David Patten on third and 12 at the Denver 13, Walker came up with an interception in the end zone.
"We got some pressure on Brady and he had to make some throws he probably didn't want to throw," Walker said.
On another throw towards Patten, Deltha O'Neal had the interception at the Denver 19 with 7:05 left.
After Walker's touchdown opened up an 11-point cushion, O'Neal grabbed his second interception with just 1:24 left.
"It wasn't the interceptions," Walker said. "The thing I liked about today was we didn't point fingers at each other. We didn't fight with each other. We just said, 'Hey, we had a lot of mistakes in the first half. But we have to stay together as a team.'"