The forward had missed the previous three games with an illness.
Jake Allen made 30 saves for the Devils (5-4-0), who have won three of their past four games. Allen, who was making his second straight start, was honored prior to the game for playing in 500 NHL games.
Artturi Lehkonen scored two goals, Cale Makar had two assists, and Scott Wedgewood made 37 saves for the Avalanche (5-4-1), who lost 3-2 at the Philadelphia Flyers on Monday and are 1-2-1 in their past four.
Evangelista scored on a wrist shot down the slot to give the Devils a 1-0 lead at 6:40 of the first period. The forward was traded to the Devils from the Nashville Predators on Sept. 1.
Gabriel Landeskog tied the game 1-1 at 14:32, scoring on a wrist shot from outside the right post. Makar took the puck at the right point, stickhandled between the legs of Timo Meier and skated past Jack Hughes before finding Landeskog alone in prime position.
Declain Chisholm gave the Devils a 2-1 lead after his snap shot from the left point deflected off the stick of Avalanche forward Brock Nelson in the slot and past Wedgewood at 12:33 of the second period. It was Chisholm's first goal with the Devils; the defenseman was acquired in a trade with the Washington Capitals on June 25.
Allen made 13 saves in the third period, including stops against Nathan MacKinnon and Makar just outside the right post at :38.
Arseny Gritsyuk pushed it to 3-1 at 4:39 of the third period, picking up the puck in the neutral zone, skating over the blue line and splitting the defense pairing of Makar and Devon Toews before scoring on a backhand.
Jesper Boqvist scored an empty-net goal at 16:05 for a 4-1 lead.
Lehkonen pulled the Avalanche within 4-2 at 16:46. He then scored his second of the game at 19:55 with Wedgewood pulled for the extra attacker for the 4-3 final.
Connor Brown had an assist in 13:54 of ice time in his season debut for the Devils, returning from a lower-body injury sustained during training camp on Sept. 28.
