Tomas Hertl scored on a first-period deflection for the Sharks, who outshot the Blues 32-23, but once again the best player on the ice was goalie Brian Elliott.
St. Louis grabs a 1-0 lead in the Western Conference Final.
The turning point in the game came in the second period when the Blues were outshot 15-5, but took the lead on a long shot from Jori Lehtera.
The goal was created off a turnover in the neutral zone and should have been handled by Sharks goalie Martin Jones.
Elliott and the Blues caught a break later in the period when the whistle blew despite Elliott not able to cover the puck.
He unsuccessfully tried to smother a long dump-in and it slowly slid between his pads and off his stick into the net, just after play had been ruled dead.
“The puck was spinning a lot and it probably just spun out,” Elliott said. “I haven’t really seen it yet, so I don’t know.”
He also stopped a furious late third period rally and robbed his college roommate at Wisconsin, Sharks captain Joe Pavelski.
“No, I have to find a way to put that in regardless of what goes on. I thought it was going in,” said Pavelski.
Once again Elliott left the opposition frustrated.