Pavelski pounced on a loose puck in the slot and flung a wrist shot past Craig Anderson at 10:24 of the extra period.
The win sends the quarterfinal series to San Jose tied 2-2. Game 5 will take place Thursday.
Anderson made 43 saves and Paul Stastny scored the only Colorado goal.
Boyle gave San Jose an early 1-0 lead with a power-play slapshot goal at1:12 of the first period.
Stastny scored on a power play at 2:37 of the second period to tie the game.
2014: The Year in Music [PHOTOS]