Curtis Brown set the tone with a goal in the opening three minutes and Ryane Clowe also scored to help San Jose improve to 80 points, one behind second-place Dallas in the Pacific Division.
The Sharks had been 0-3-1 in their previous four games and won only two of the first seven meetings with the Stars this season, but Nabokov didn't have much trouble earning his fifth shutout of the season.
San Jose had dropped its past six games to the top eight teams in the Western Conference and was in a 2-6-1 slump before beating Dallas in the teams' final regular-season meeting.
Marty Turco had 14 saves for the Stars, 12-3-4 in their previous 19 games including an 8-1-2 run at home to jump past the Sharks in the standings.
Turco saw Sharks parked in front of the net for much of the game, creating traffic and ready for rebounds.
Brown scored his eighth goal of the season 2:38 after the opening faceoff on the game's first shot, a wrister from the inner edge of the left circle. It was San Jose's only shot of the first period while Dallas was unable to beat Nabokov on nine shots.
The Sharks turned up the offensive pressure in the second period, extending their lead to 3-0.
Clowe backhanded a rebound past Turco at 11:27 of the second period to give the Sharks a two-goal edge.
San Jose made it 3-0 at 15:58 of the second period when Pavekski beat Turco on a goal-mouth scramble. Pavelski added his 14th goal of the season off a two-on-one with Clowe with 1:43 to play for a 4-0 advantage.
Notes: D Mattias Norstrom made his debut for the Stars after being acquired last Tuesday in a trade with the Los Angeles Kings. ...San Jose C Patrick Marleau (upper-body injury) was scratched for the third straight game, but D Scott Hannon returned to the lineup after missing the previous two games with a leg injury. ...Dallas RW Krys Barch missed the third period with a lower-body injury.