Buffalo lost its opener last week when Chad Morton returned the overtime kickoff for a touchdown and a 37-31 victory for the New York Jets.
But the Bills bounced back behind Bledsoe, who completed 35 of 49 yards for a career-high 463 yards. His previous career best was 426 yards in a game against the Vikings with the New England Patriots in 1994.
"This helps us build confidence that we're doing the right thing and shows the young guys that we're doing the right thing," Bledsoe said.
The Bills took over for its third possession of the extra session at their own 25-yard-line and Bledsoe immediately found tight end Jay Riemersma for a 28-yard gain into Minnesota territory. On the next play, he found a wide-open Price on the left side and Price cut back and ran untouched into the end zone for his second touchdown of the game.
"We had been running a hook pattern all game," Price said. "The guy (CB Brian Williams) started jumping late, so we called a hook and up. It was me and him one-on-one, I just had to beat the safety. It was improvised."
Bledsoe credited offensive coordinator Kevin Gilbride for calling the play on Price's game-winning score.
"It was a great call by Kevin," Bledsoe said. "We had been throwing those hook routes to Peerless through the course of the game. He called the hook and up and Peerless beat his guy."
The Vikings appeared to have the game won in regulation when Moe Williams scored on a two-yard run with 26 seconds left for a 39-36 lead. But Bledsoe was able to set up the game-tying field goal by driving the team 29 yards in 18 seconds.
The Bills started on their own 35 and Bledsoe had completions of 13 yards to Larry Centers and eight yards to Josh Reed. Bledsoe hit Price for an eight-yard gain and Mike Hollis came on and booted a career-long 54-yard field goal that hit the crossbar and bounced through as time expired.
"I've got a lot of pride in kicking long field goals," Hollis said. "I don't have the best leg in the world, it really forces you to finish the kick."
The Bills started on their own 35 and Bledsoe had completions of 13 yards to running back Larry Centers, eight yards to rookie Josh Reed and eight yards to Price before Hollis' tying field goal.
Hollis, who also booted a 52-yarder in the first quarter, had a chance for a game-winner on Buffalo's second possession in overtime but missed a 45-yard attempt.
The kicking game let down Minnesota as Doug Brien missed a pair of extra points that proved to be costly.
"High school kids make those," Brien said. "I'm so disgusted with myself."
Bledsoe and Daunte Culpepper put on an offensive show for most of the game as the opposing quarterbacks had no trouble shredding the two defenses. Culpepper completed 25 of 45 passes for 281 yards and three touchdowns and ran for another. However, he fumbled three times, which led to 13 points for the Bills.
"I wish we could play the whole game over," Culpepper said.
A 61-yard punt return by D'Wayne Bates led to Culpepper's two-yard touchdown pass to Randy Moss that opened the scoring in the second half. That gave Minnesota a 20-13 lead and set off a wild flurry of points.
Buffalo's Charlie Rogers returned the ensuing kickoff 90 yards for a touchdown to tie the game.
"Two 50-yard field goals in the ball game, none bigger that the one that tied it up and put us in overtime," Buffalo coach Gregg Williams said. "He's (Hollis) a solid kicker and really a calming influence on the field. Charlie Rogers too, he matched the punt return we gave up. There were a lot of momentum changes."
Hollis booted a short field goal to give Buffalo the lead before Culpepper led an eight-play 63-yard drive that culminated in a 29-yard touchdown to Bates for a 26-23 lead. Brien missed the extra point.
The Bills came back when defensive end Aaron Schobel sacked Culpepper, who fumbled and tackle Ron Edwards came up with the ball in the zone for a 30-26 advantage.
"Just fall on it, pretty much was all I was thinking," Edwards said. "I saw it pop out, I had to get on it."
Culpepper led another long drive of 82 yards that included four carries by Williams for 41 yards. On forth and two on the Bills' five-yard-line, Culpepper found Derrick Alexander for a touchdown and a 32-30 advantage. Brien was wide on the extra point.
"You can't miss PATs in this league and we missed two, and that shouldn't happen to anybody," Vikings coach Mike Tice said.
Bledsoe came right back and needed just 4:13 to put Buffalo back on top. Reed had a pair of catches for 44 yards in the drive and Price scored on a three-yard reception for a 36-32 edge.
The Vikings blew a lead for the second straight game after they let a 10-point lead in the fourth quarter slip away in last week's season-opening loss at Chicago.
The big day for Bledsoe resulted in huge numbers for his receivers. Price caught 13 passes for 185 yards, Reed had eight receptions for 110 and Eric Moulds caught eight for 86.
"Peerless had a huge game today, and Josh Reed showed that its pretty tough to double Eric Moulds and not give up plays in the middle," Buffalo coach Gregg Williams said.
Bledsoe surpassed the 30,000-yard mark with a 14-yard pass to Price in the second quarter, becoming the third-fastest quarterback to do so. Bledsoe did it in his 126th game. Only Dan Marino (114) and Warren Moon (125) did it faster.
Williams carried 17 times for 102 yards as Minnesota held a 211-31 advantage in rushing yards. The Vikings had 447 yards of total offense.