San Jose scored 4:42 in when a Brent Burns shot from the right point was tipped in by Handzus.
Pavelski made it a 2-0 game with 3:28 to play in the first on his 19th of the season.
Dallas cut the lead to one on Ott's eight of the year at the 12:41 mark of the second. That power-play goal stopped a scoreless streak by San Jose that lasted for 190 minutes and 51 seconds, the longest mark in franchise history
Just over two minutes later, though, the Sharks got the goal back as Couture redirected a Burns shot and Thornton made it a 4-1 game two minutes later with his 11th of the year.
Benn scored 6:22 into the third to get Dallas back within two, but Clowe's goal with 8:26 to play sealed the win for San Jose.
San Jose plays at Phoenix on Saturday...Dallas hosts Minnesota on Saturday...San Jose has won five straight against Dallas, including all three games this season.