Damphousse scored his seventh goal of the season just 24 seconds after the Thrashers tied the game, 2-2, midway through the second period. He took a pass from Marco Sturm and threw a slap shot from the right faceoff circle past the low left side of Atlanta goaltender Damian Rhodes to give the Sharks the lead.
Rookie Dany Heatley scored his fourth goal of the season 9:35 into the period. He charged down the right side and wristed a shot from the right faceoff circle into the upper left side of the net.
Less than a minute later, Patrik Stefan tied the game with his first goal of the season. Stefan, who been out for four weeks after suffering a broken jaw against Boston on Oct. 6, poked his own rebound through Nabokov's legs.
Atlanta did not threaten in the third period, managing only three shots.
San Jose's Owen Nolan made it 4-2 with 2:18 left in the second period before Niklas Sundstrom scored an empty-net goal with 14 seconds remaining in the contest.
The Sharks have won three in a row for the first time since Feb. 10-16.