Armstrong's first goal gave the Leafs a 1-0 first-period lead and Toronto extended the advantage to 3-0 with second-period scores by John Mitchell and Nikolai Kulemin.
Armstrong added a third-period goal and Gustavsson blanked the Devils on 4-of-5 power-play opportunities as the Leafs broke a three-game losing streak.
The reeling Devils, meanwhile, lost for the fifth straight time, including two straight under returning Coach Jacques Lemaire.
Rod Pelley got New Jersey's only goal and Martin Brodeur turned aside 11-of-14 shots over two periods before being pulled in favor of Johan Hedberg, who let in one goal on eight shots in the third.
The Devils lost for the 10th time in 11 December games.