Marcus Sorensen scored in the second period for San Jose (2-2-0), which avoided a third straight loss and gained a split in the two games with the Blues after losing 5-4 here Monday.
Tomas Hertl scored the only goal of the shootout in the fourth round against Blues goalie Jordan Binnington, who made 37 saves.
"I think after last game, both teams wanted to tighten up defensively," Sharks captain Logan Couture said. "You go back two games ago, they gave up eight, we gave up five in Arizona. We wanted to tighten up, they wanted to tighten up defensively. We still had a few breakdowns, they still had a few breakdowns. It's early in the season; that's going to happen, but I think in the third period, we played the style of hockey that we wanted to play. ... I liked our third period for sure."
The Sharks outshot the Blues 17-3 in the third and had two power-play opportunities but couldn't score against Binnington.
"It's a 1-1 game and just compete," Binnington said. "Our kill hasn't been doing so well coming into this game, so we know we wanted to have a good penalty kill, special teams. I think we had a good night in that department. But, you know, not the outcome we wanted."
Brayden Schenn scored for the Blues (2-1-1).