In the first meeting between the teams since Anaheim took the Stanley Cup in five games last season, the Ducks also got a goal from Todd Bertuzzi.
The victory pulled them to within four points of Dallas for first place in the Pacific Division. The Stars did not play Monday.
Christoph Schubert scored and Martin Gerber stopped 28 shots for the Senators, who lost for the fourth time in their last five games.
Bertuzzi opened the scoring, beating Gerber with a one-timer at 11:58 of the first period. The Ducks scored what turned out to be the game-winner three minutes later when Niedermayer's shot on goal rebounded toward Perry, who put it into the net.