"The relief is there, it's (finally) over," San Jose coach Todd McLellan said. "Now, we can't let our game slip."
Patrik Berglund scored his team-high ninth goal for St. Louis in the first period. He has tallied in the past four games, a career best.
Thornton then tied the game early in the second period jumping on a rebound from close range.
San Jose, which outshot the Blues 9-5 in the third period, held St. Louis without a shot for the first 12:17 of the final period.
The Sharks were playing for the first time since Friday while St. Louis arrived home at 6:30 a.m. on Tuesday after a 14-hour travel delay in Vancouver.
Yet the Blues weren't using fatigue as an excuse.
"Too many people not pulling their weight," Coach Ken Hitchcock said. "Too many passengers."
NOTES: Kennedy led all players with five shots on goal. ... This was the first meeting between the teams since St. Louis beat San Jose in five games in the Western Conference playoffs last season. ... G Jaroslav Halak is expected to start for the Blues on Wednesday in Colorado. ... San Jose played the fourth game of a six-game road trip. The Sharks return home Jan. 26 to face Colorado.