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.
"It’s a bummer, obviously," Ducks defenseman Jackson LaCombe said. "I thought we played well, and we had a few good chances at the end to tie it up but that didn't happen. So we just got to move on to the next game."
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.
"We've been playing together for 15 years, so it's nice to have him back," Vlasic said. "He made a nice play and I joined the rush."
LaCombe tied it 1-1 just 15 seconds later at 15:21 with his first NHL goal. 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 Henrique made it 3-2 just 24 seconds later at 19:56 when Terry set him up from behind the net.
The Ducks outshot the Sharks 20-7 through two periods.
"It doesn’t matter how many shots you have, it's the quality of the shots," Ducks coach Greg Cronin said. "And we actually had quality shots we didn't take. Give them credit, they did an unbelievable job blocking shots, and they stayed with it.”