Allen, a rookie making only his seventh NHL start, continued a hot streak by stopping 18-of-19 San Jose shots during a furious second period for the Blues.
Stewart tallied in the first period and added an empty-netter as St. Louis won for the third time in four games.
Antti Niemi made 17 saves for San Jose.
Wisconsin business offering 'therapeutic cuddling' forced to close
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph