Ivan Barbashev scored 35 seconds into regulation to help lead the Blues to a 2-1 win over the Sharks in St. Louis.
Tyler Bozak also scored in the first for St. Louis.
Jordan Binnington stopped 29 of 30 shots for the Blues, who tie the Western Conference Finals at two games apiece.
Tomas Hertl scored the lone goal for the Sharks. Martin Jones allowed two goals on 22 shots for San Jose.