The Devils remained winless in three home games this season despite firing 42 shots at Colorado's Craig Anderson.
Colorado's Cody McLeod received a game misconduct penalty in the first period for driving a New Jersey player into the boards, but the Devils could not take advantage of the 5-minute power play that followed.
The Avalanche managed a 1-0 lead after one period despite being outshot 17-3 in the stanza.
Stewart scored on a slapshot 4:31 into the third to give Colorado a 3-1 advantage. Ilya Kovalchuk brought the Devils within one with 11:11 to play in regulation, but Anderson was solid the rest of the way.
Martin Brodeur gave up three goals on 22 shots to take the loss.
Matt Taormina scored a power-play goal for the Devils in the second period, the first of his NHL career.
Colorado has won three of its four games this season.
Celebrity Families of 2014 [PHOTOS]