Anaheim did not lead until Niedermayer put a backhander past Miikka Kiprusoff to bring the Ducks their second win over the Flames in four days.
Niedermayer also scored midway through the second period on the power play to knot the game at 1-1.
Calgary regained the lead late in the second, but Anaheim tied it again 2:05 into the third on Brendan Morrison's goal.
Jean-Sebastien Giguere made 21 saves to win for only the second time since Jan. 11. Giguere had lost four consecutive starts before getting the win over Calgary in the opener of their home-and-home series Saturday.
Kiprusoff saved 37 of 40 shots.
Costly malfunction causes beer flood at Boston-area brewery
Wisconsin business offering 'therapeutic cuddling' forced to close