Favre's touchdown tosses were for 1 yard to Visanthe Shiancoe and 3 yards to Percy Harvin and Peterson scored on a 27-yard run.
The veteran quarterback, who set an NFL record with his 271st start in a regular-season game, was 23-of-27 for 155 yards.
Peterson ran 27 yards for a touchdown and accumulated 92 yards rushing.
The Vikings (2-0) have won 14 of their last 15 games against Detroit.
The Lions' Matthew Stafford passed for 152 yards, including an 8-yard touchdown to Calvin Johnson, but was intercepted twice.
Kevin Smith carried 24 times for 83 yards for Detroit (0-2)..
Swim Week Miami Beach 2014 [PHOTOS]