Halak joined the New York Rangers' Henrik Lundqvist and Jonathan Quick of Los Angeles at the top of NHL's shutout list, turning aside all 25 shots he saw as St. Louis extended its franchise-record home point streak to 19 games.
Alex Pietrangelo scored on a first-period power play and added an empty-netter. David Perron also found the net for the winners.
Antti Niemi absorbed the defeat despite making 25-of-27 shots for the Sharks, who opened a nine-game road trip with the loss.
Niemi fell to 0-4-0 in his last four games against St. Louis.