Jones was pulled early in the second period Friday after giving up three goals in a 5-4 overtime road loss to the Vegas Golden Knights, but he bounced back for his 10th victory of the season.
Steve Mason started for the Jets (14-6-3) but left the game after the first period because of an upper-body injury. He gave up two goals on 13 shots.
Mason was hit in the mask by Jannik Hansen's slap shot at 8:43 of the first period, but Jets coach Paul Maurice said he "was fine" initially.
"By the time he got off the ice [for the first intermission], he was not feeling right," Maurice said. "And for us, that was enough. He has to come out. We pulled him as a precaution. We'll get him looked at [Sunday] and get a good idea of how he's feeling."
Connor Hellebuyck relieved Mason at the start of the second period and made 20 saves.
Heed, who was a healthy scratch the previous two games, gave the Sharks a 1-0 lead with a power-play goal at 11:30 of the first period. Kevin Labanc faked a shot from the right circle and sent a behind-the-back pass to Heed in the high slot. Heed scored on a slap shot for his third goal of the season.
"Sometimes it's good to watch the game from the side and get another view of it," Heed said of being scratched. "Took something out of it and tried to do something better."
Couture made it 2-0 when he scored on a rebound with 16 seconds left in the first period.