"The players and coaches have great pride in what we're doing," Giants quarterback Eli Manning said. "We just had to keep going, get rid of some of the mistakes, and play the way we need to play."
Peterson, the league's MVP last season and a 2,000-yard rusher, was held to 28 yards five days after his 2-year-old son was buried in South Dakota. The man accused in the death was indicted on second-degree murder and manslaughter charges, prosecutors said Monday.
Peterson was not helped by a rusty Josh Freeman, making his debut as Vikings quarterback after being signed as a free agent when Tampa Bay cut the 2009 first-round draft pick. Freeman frequently missed open receivers, and several of his throws sailed yards beyond his targets.
Josh Brown kicked three field goals and Rueben Randle caught a 24-yard TD pass for New York (1-6).
"For us, we can't look too much past a win and a step in the right direction," defensive tackle Cullen Jenkins said. "We can't look beyond the next step."
Marcus Sherels provided Minnesota's points with an 86-yard punt return, but his fumble without being hit during a runback midway in the third quarter set up New York at the Vikings 3.
Peyton Hillis, signed last Wednesday with the Giants in dire need of running backs, surged in from the 1 for a 17-7 lead New York's biggest in 2013.
The lead grew on Brown's 23-yard field goal to finish off a 16-play, 75-yard drive, and to 23-7 on his 36-yarder. Another Vikings mistake handed those points to the Giants: Rookie Sharrif Floyd, a defensive tackle of all things, fumbled at Minnesota's 18 while returning a short kickoff.
"We needed to get one on the board," defensive end Justin Tuck said. "Hopefully, tonight is something we can build off. It's still a long way to climb out of this hole. But this was something that we could get the ball rolling."
The Giants controlled the clock and the ball for most of the opening quarter and led 3-0 when Sherels broke his spectacular punt return the third against the Giants this season. He sped down the left sideline virtually untouched, then twice faked out punter Steve Weatherford. By the time Weatherford reached Sherels, it was at the goal line where Weatherford brought him down with a horse-collar tackle.
Minnesota had a total of 8 yards on punt runbacks heading into Monday night. But Sherels set a team mark with 119.