Couture missed the first 45 games of the season with a lower-body injury. The San Jose captain had 67 points (27 goals, 40 assists) in playing all 82 games last season.
Fabian Zetterlund and Tomas Hertl each had a goal and an assist, and Kyle Burroughs and Jan Rutta each scored his first goal of the season for the Sharks (11-31-4), who had lost three straight. Mackenzie Blackwood made 32 saves.
Adam Henrique had a goal and an assist, and Troy Terry had two assists for the Ducks (15-29-1) who have lost two straight and four of their last five. John Gibson made 14 saves.
Filip Zadina appeared to put the Sharks ahead at 17:08 of the first period, but the goal was overturned after the Ducks successfully challenged for offside.
Marc-Edouard Vlasic put San Jose ahead 1-0 at 15:06 of the second period when Couture set the defenseman up for a tip-in.
Jackson LaCombe tied it 1-1 just 15 seconds later at 15:21. Blackwood was initially credited with a save, but video review determined the puck had crossed the line.
Burroughs put the Sharks back ahead 2-1 at 17:33 when Hertl set him up for a wrist shot in front of the net.
Zetterlund increased the lead to 3-1 at 19:32 before Adam Henrique made it 3-2 just 24 seconds later at 19:56 when Troy Terry set him up from behind the net.
The Ducks outshot the Sharks 20-7 through two periods.
Rutta made it 4-2 at 12:15 of the third period with a wrist shot through traffic. It was his first goal since being traded to the Sharks from the Pittsburgh Penguins on Aug. 6 as part of the Erik Karlsson deal.
Mason McTavish made it 4-3 at 15:11 when he scored on the power play.
Hertl scored into an empty net at 19:53 for the 5-3 final.
Story by Chelena Goldman/NHL.com Independent Correspondent