Addai and Reggie Wayne hooked up on a 22-yard pass early in the fourth quarter, giving the Colts (7-0) what turned out to be the winning touchdown. A 2-point conversion attempt failed.
Stover's kicks were from 38, 33, 32 and 40 yards.
Peyton Manning threw for 347 yards for Indianapolis, completing 31-of-48 throws. It was his sixth 300-yard passing game this season.
Addai carried 20 times for 62 yards in addition to throwing the first scoring pass of his career.
Frank Gore ran 64 yards for a touchdown and Alex Smith threw an 8-yard scoring pass to Vernon Davis for San Francisco (3-4).
Smith, who replaced Shaun Hill as the 49ers' starting quarterback, completed 19-of-32 passes for 198 yards and was intercepted once.