Ducks goalie Ilya Bryzgalov made 29 saves for his first preseason victory.
Dave Scatchard led the Coyotes with a goal and an assist, and goalie Curtis Joseph finished with 29 saves in his first full preseason game.
Niedermayer scored on a power play at 7:15 of the first period by redirecting Andy McDonald's slap shot from the right point.
Perry gave Anaheim a 2-0 lead at 5:31 of the second period just as the Coyotes defused the Ducks' 5-on-3 advantage. Perry took the puck from Dustin Penner and stuffed it under Joseph.
Scatchard narrowed the deficit to 2-1 at 10:28 of the third period. Marchant extended the Ducks' lead back to two goals at 15:12 before the Coyotes' Keith Yandle ended the scoring with a power-play goal at 19:58.
Ducks forward Teemu Selanne left the game at 3:44 of the first period after taking a stick to the mouth. Selanne bled from the mouth before going to the locker room for stitches.