Pavelski's second goal midway through the third period broke a 2-2 tie and proved to be the game-winner, lifting the top-seeded Sharks to a six-game triumph over the eighth-seeded Avalanche.
Colorado briefly took the lead on a goal from Brandon Yip early in the third period, sending the Pepsi Center crowd into a frenzy, but San Jose's Dan Boyle quickly answered, tying the game at two goals apiece less than three minutes later.
Pavelski assisted on Boyle's tally to finish the game with three points.
Evgeni Nabokov benefited from a strong Sharks defense and needed to make only 16 saves in the series-clinching win while Devin Setoguchi and Douglas Murray iced the victory with empty-net goals.
Marek Svatos scored for Colorado and Craig Anderson finished with 30 saves as the Avalanche's season came to an end.