Jonathan Cheechoo also scored for the Sharks, who won their second game in two nights following three straight losses. San Jose handed the Blackhawks their fifth consecutive defeat (0-3-2) and third straight in regulation. Nabokov was not heavily tested by sluggish Chicago in earning his 31st career shutout.
For San Jose, Thursday's game was the seventh in an eight-game road trip. The Sharks are 4-3-0 so far on the trip.
Chicago's Patrick Lalime started in goal for the third time in the past four games and made 21 saves.
Lalime entered the game with a 0.98 goals-against average. However the Blackhawks, who have three goalies on their roster, may be showcasing Lalime prior to Tuesday's trade deadline.
The start was only Lalime's fourth overall this season. He missed the first half of the season following surgery to repair a herniated disc.
Thornton opened the scoring with a power-play goal at 9:58 of the first period. He beat Lalime under the arm on the stick side with a shot from the left circle.
The Sharks entered the game with the NHL's best power-play, converting at 23.3 per cent.
Cheechoo extended San Jose's lead to 2-0 at 4:27 of the second. After Thornton centred the puck into the slot, Cheechoo turned and fired a shot past Lalime on the glove side.
Blackhawks forward Martin Lapointe inadvertently helped Nabokov preserve his shutout on an unusual play with 8:04 left in the second.
Chicago's Lasse Kukkonen beat Nabokov high on the glove side with a screened drive from the slot. But the shot hit Lapointe, who was behind Nabokov in the crease, on the shoulder. The puck then fell to the ice and Nabokov covered up with his glove.
Nabokov faced eight shots in the third, but only a couple were from close range.
Notes: For the second time in three games, Blackhawks top goalie Nikolai Khabibulin didn't dress. Lalime was backed up by Brian Boucher. ...Chicago rookie D Cam Barker sat out with a bruised ankle. ... Sharks G Vesa Toskala missed his second game with the flu and a groin injury. Nabokov was backed up by rookie Nolan Schaefer for the second straight game. San Jose D Rob Davison, D Josh Gorges and LW Ville Nieminen were healthy scratches. ... Both teams had played on Wednesday night and had to travel to Chicago for Thursday's game. Chicago fell 4-2 at Detroit and San Jose won in a shootout at Washington, 3-2.