Kahkonen won his second consecutive game after going winless in his first seven starts after coming over in a trade with Minnesota on March 21. The Finland native won for just the third time since Feb. 20.
"We made a lot of mistakes early on in the game," Meier said. "There was a stretch for 10 minutes that was horrible where we had a lot of turnovers. And he really stood up for us and bailed us out."
The Blackhawks have brought out the best in Kahkonen this season. He beat them on back-to-back nights in January while with the Wild, stopping 68 of 72 shots in those games.
He was busy in the first period, making nine saves, and he denied Chicago on a dangerous 2-on-1 opportunity in the second.
The Blackhawks, who have lost 10 of 12, were criticized by interim coach Derek King after mustering a season-low 16 shots on goal in Thursday's loss to the Los Angeles Kings. They outplayed San Jose in the first period but still found themselves trailing.
"I thought we played well," Chicago defenseman Seth Jones said. "It's not going to be mistake-free, but those big mistakes that end up in the back of our net, that really hurt us."
San Jose was outshot 9-4 in the first but grabbed a 1-0 lead on Weatherby's first NHL goal since Feb. 24. Sasha Chmelevski's shot on goal ricocheted to teammate Scott Reedy, who fed Weatherby for an easy scoring opportunity.
Meier made a steal and fed Hertl on a perfectly executed 2-on-1 for a 2-0 lead early in the second. Then Meier scored one of his own later in the period, a sequence that started when he stole a pass from rookie defenseman Alex Vlasic.
Meier, San Jose's leading scorer, hadn't registered a point over the previous three games. Hertl, second on the team in goals, had just one point in that same span.
"We need them to play their best, along with myself and other guys if we want to get where we need to be," center Logan Couture said. "It's not fair to put the blame on those two when we're not scoring."
Johnson got one back for Chicago with his third goal of the season late in the second, but Bonino's power-play goal at 6:19 of the third ended any Chicago comeback hopes.
A WELCOME RETURN
Left wing Alexander Barabanov made his presence felt after returning from an upper-body injury that sidelined him the previous four games. He assisted on Meier's second-period goal and was part of a rejuvenated effort by San Jose's top line.
"I think he thinks the game at a high level," Couture said. "He's not overly fast, but he gets into the right spots. He's a very good player."
Collin Delia, Chicago's backup goalie, was available Saturday after he left Thursday's game early due to cramping.
Blackhawks: Host Philadelphia on Monday to begin their final homestand.
Sharks: Play at Vegas on Sunday.