Detroit botched a field-goal attempt on the opening drive when rookie holder Sam Martin dropped a perfect snap.
Peterson's first touchdown made it 7-0, and the 2012 Associated Press Most Valuable Player looked well on his way to another huge game after rushing for 2,097 yards last season.
Detroit coach Jim Schwartz went for it on fourth-and-1 in the second quarter, only to have Joique Bell's run negated by Brandon Pettigrew's holding penalty.
The Lions settled for a field goal to make it 7-6.
Detroit linebacker DeAndre Levy appeared to have returned an interception for a touchdown, but Ndamukong Suh was called for an illegal low block during the return against center John Sullivan, who was well behind the play.
"I spoke to him, we're good," Suh said. "I wasn't by any means going for his knees. He knows that. We had a great conversation about it at halftime. He understood. My end point was his waist, to cut him off."
Lions quarterback Matthew Stafford threw an interception on the next play, and Minnesota took advantage, going ahead 14-6 on Peterson's short burst.
Ponder's second interception of the game — with 2:14 left in the second quarter — proved costly when the Lions finally reached the end zone on Bell's 2-yard dive with 10 seconds left in the half.
Bell leaped over a pile and extended his arms, and although the ball was jarred loose, a video review showed it had reached the goal line.
After a 1-yard touchdown run by Bell in the third quarter gave the Lions a 20-14 lead. Bush's long touchdown made it 27-17, although the Vikings answered with Ponder's 4-yard scoring pass to Peterson.
Minnesota was still in decent shape at the start of the fourth, but two more turnovers did the Vikings in.