The game marked the St. Louis debut of quarterback Sam Bradford, the NFL's No. 1 draft choice this year.
Bradford, who has become one of the highest-paid players in league history, completed 6-of-13 passes for 57 yards.
With Brett Favre's future in doubt, Minnesota started Tarvaris Jackson at quarterback. Rosenfels came in early in the game, however, and completed 23-of-34. He threw a 2-yard scoring pass to Logan Payne early in the second quarter to forge a 7-7 tie.
Rosenfels then hit Garrett Mills with a 65-yarder midway through the second and found Marko Mitchell with a 71-yarder late in the third.
The St. Louis touchdown came on a 93-yard punt return by Danny Amendola.