The Sharks won for just the second time in six games with two ties over that stretch as they improved to 18-5-2-2 all-time against Winnipeg. The Jets had won five of their previous six and 10 of their last 13.
Couture scored a short-handed goal on a breakaway at 13:13 of the second period for his 13th goal of the season that gave the Sharks a 3-0 lead. Couture took the puck from just past the San Jose blue line. He faked a shot as he approached goalie Connor Hellebuyck and then backhanded the puck into the net.
Couture scored his goal just outside the crease after he rebounded a deflection with 16 seconds left in the first period.
Tomas Hertl scored an empty-netter at 16:50 of the third.
NOTES: Sharks C Melker Karlson participated in Saturday's practice but missed his fourth game with an upper body injury. . Jets Fs Shawn Matthais and Marko Dano and D Tucker Poolman were healthy scratches.
Winnipeg: Hosts Minnesota on Monday.
San Jose: Opens a four-game road trip in Philadelphia on Tuesday.