Elliott led the NHL during the regular season in goals-against average (1.56) and save percentage (.940). He allowed three goals over the first three games of the opening-round playoff series before turning in a near-perfect performance in Game 4.
The Blues own a 3-1 lead in the series and will attempt to close out the Sharks Saturday in St. Louis.
Joe Thornton spoiled Elliott's shutout bid, but Elliott hung on to make 24 saves and pick up his third career playoff victory.
Antti Niemi allowed the two St. Louis goals on 24 shots.
B.J. Crombeen opened the scoring for the Blues 7:12 into the contest and what turned out to be the game-winning goal came from Andy McDonald on the power play with 8 minutes to go in regulation.
In contrast to many of the playoff games this year, this one featured just hockey and no brawling. There were just seven 2-minute penalties called in the contest.