Milan Michalek and Mark Bell scored for the Sharks, who matched the best start in franchise history at 5-1 while preventing Dallas from equalling its club-best 6-0 start in 1996.
Marty Turco stopped 21 shots for the Stars, who controlled play for long stretches against the team that finished right behind them atop the Pacific Division standings last season, but couldn't earn one more win in the finale of an impressive four-game road trip.
Dallas' loss left Buffalo and Minnesota as the NHL's only unbeaten teams.
Nabokov, the Sharks' starting goalie since 2000, has two shutouts and a six-goal loss so far in his uneasy platoon with Vesa Toskala, who has won all three of his starts. With ample help from his defence, Nabokov added his 29th career shutout to a 2-0 win over the New York Islanders in his first start of the year.
San Jose opened a three-game homestand against the Western Conference's three current first-place teams by holding Dallas without a point for just the fourth time in the division rivals' last 20 meetings.
Michalek got the Sharks' first goal late in the first period with his typical puck awareness, batting a pass from rookie Matt Carle over Turco's head and into the net. The second-year forward leads the Sharks with five goals after topping the NHL with seven pre-season goals.
The Stars dominated the second period, peppering the San Jose net with a 14-4 shot advantage - but Nabokov remained solid, making two stunning kick saves.
Bell, back on the Sharks' top line after missing their three-game road trip with a groin injury, scored late in the second period when Jonathan Cheechoo drew Turco and the defence before flipping a perfect pass to his linemate in front.
Nabokov made his best save with 4 1/2 minutes to play, doing the splits across his crease for an unbelievable right-pad stop on Jeff Halpern, who thought he had an open net.
Nabokov once scored a goal against Vancouver, and he took another shot at the Stars' open net in the closing seconds - but Sergei Zubov kicked it away at center ice.
Notes: Before the game, San Jose activated Bell from injured reserve and put LW Ryane Clowe back on IR with a foot injury. ... Sharks captain Patrick Marleau's wife, Christina, gave birth to their first child Monday, a boy named Landon. ... The Sharks opened 5-1 in 1994, but went winless in their next five games. San Jose can surpass that start against Detroit on Thursday night.