Matthews and Patrick Marleau scored for the Maple Leafs (26-18-5). Andersen stopped 23 shots in defeat.
Colorado began its winning streak with a 4-3 overtime victory on Dec. 29 at home against Toronto.
Bourque opened the scoring 2:19 into the game, banging in the rebound of a shot by Tyson Jost that Andersen took in the chest and couldn't corral.
Marleau tied it 19 seconds into the second, firing a one-timer from the top of the faceoff circle over Bernier's glove on a setup from Leo Komarov.
Matthews thought he gave Toronto the lead on a goal-mouth scramble, tapping in a loose puck after it hit Zach Hyman in the skate and skipped behind the Avalanche netminder. But Colorado challenged for goalie interference and the call was overturned, angering coach Mike Babcock on the Maple Leafs' bench.
Matthews scored off William Nylander's rebound on his next shift after the disallowed goal, and made sure everyone knew it was a good goal by pointing at the net like an official and showing some rare emotion as he celebrated at 9:17.
The lead didn't last long, though, as Yakupov took a cross-ice pass from Alexander Kerfoot and beat Andersen at 10:51.
Game notes Nathan MacKinnon, chosen the NHL's first star of the week earlier in the day after posting four goals and six points in three Colorado wins, had his nine-game point streak snapped. ... Just before the game, the Maple Leafs announced that defenseman Morgan Rielly was placed on injured reserve. He missed his second straight game because of an upper-body injury sustained Thursday against Philadelphia.
Avalanche: Will try to extend their winning streak to 11 games Tuesday night in Montreal.