Terry had missed the previous nine games because of an upper-body injury.
Leo Carlsson had two goals and an assist, and Chris Kreider had two assists for Anaheim (37-27-3), which had lost two in a row, including 2-0 at the Ottawa Senators on Saturday. Lukas Dostal made 27 saves.
Nick Suzuki had a goal and an assist, Cole Caufield scored, and Jacob Fowler made 24 saves for Montreal (36-20-10), which was coming off a 4-2 loss to the San Jose Sharks on Saturday.
Terry tied it 3-3 at 15:39 of the second period. He kicked Kreider’s cross-ice pass to his stick in the right circle and lifted a backhand over Fowler’s glove.
Gauthier put the Ducks in front 4-3 with 2:30 remaining in the third period. Jeffrey Viel won a battle along the boards with Kaiden Guhle and sent a backhand pass to Gauthier, who scored five-hole from the right circle.
Carlsson gave Anaheim a 1-0 lead at 7:46 of the first period after finishing a pretty passing play on a 3-on-2 rush. Terry began the sequence by passing across to Kreider, who then fed the puck down low to Carlsson for a tap-in into the open net at the right post.
Carlsson scored his second goal of the game 27 seconds into the second period to make it 2-0. He won a face-off in the left circle before flaring out into the high slot and scoring with a one-timer off a pass from Jackson LaCombe.
Alex Newhook cut it to 2-1 at 1:33 with a one-timer from the right circle off a pass from Lane Hutson.
Caufield then tied it 2-2 with his 39th goal of the season at 2:33. He took a stretch pass from Noah Dobson, skated down the left side on a rush and snapped a shot past Dostal's glove from the circle.
Suzuki put Montreal ahead 3-2 at 13:06. Juraj Slafkovsky skated the puck out of the defensive zone and through the neutral zone before passing over to Suzuki, who beat Dostal under his glove from the right circle.
Defenseman John Carlson played his first game with Anaheim since being acquired in a trade with the Washington Capitals on March 6. He was plus-1 in 22:59 of ice time.
Canadiens forward Kirby Dach left the game with an upper-body injury shortly after he fell to the ice following a hit by Viel at 3:30 of the first.
