Ponder, who went 21-of-35 through the air for 198 yards, also ran for a score as the Vikings (2-1) rebounded from a last-second loss to the Indianapolis Colts in their previous game.
Rudolph grabbed five passes in all, finishing with 36 yards, while Percy Harvin hauled down nine Ponder tosses for 89 yards.
Adrian Peterson paced Minnesota's ground game with 86 yards on 25 carries.
The 49ers (2-1) were led by Alex Smith, who completed 24-of-35 passes for 204 yards with a touchdown and an interception.
Frank Gore gained 63 yards on 12 carries but also fumbled in the loss.
Notable deaths of 2014 [PHOTOS]