Devin Setoguchi picked up two goals, including the game-winner at 14:11 in the third period, to give the Western Conference-leading Sharks their fourth win in a row.
"With (Thornton) out we need some secondary scoring," Setoguchi told reporters. "I know that's my job and it was good to get a couple tonight and get on the board for us."
Setoguchi opened the scoring in the first period before Colorado took a 2-1 lead on goals from Peter Mueller and Kevin Porter in the second. Jed Ortmeyer tied the score at 2-2 with under two minutes to play in the period.
In the third period, San Jose's Dan Boyle and Colorado's Mueller traded goals before Setoguchi netted the winner.
Colorado (41-27-7) have lost five of their last six, slipping to eighth in the West.
San Jose had endured a six-game losing streak prior to their recent string of wins and Sunday's victory was coach Todd McLellan's 100th regular season triumph in just two seasons.
Backup goaltender Thomas Greiss made 42 saves to secure the win while Colorado netminder Craig Anderson had 28 stops.
"We came up a little short," said Colorado coach Joe Sacco.
"I think if we play like we did tonight down the stretch here, we'll be fine. That's how we have to play, with that desperation. It's a word that's overused this time of the year but it's true."
(Reporting by Jahmal Corner in Los Angeles; Editing Peter Rutherford)