Robert Bortuzzo, Vladimir Sobotka and Patrik Berglund also scored for the Blues, who have won consecutive games after losing nine of 10. They began the night three points out of a playoff spot in the crowded Western Conference race.
Anaheim pulled to 3-2 at 6:15 of the third period when Chris Kelly sent a wrist shot from beyond the circle that deflected off Grant and sailed past Allen for his ninth goal.
They opened the scoring 17:33 into the first period when a quick pass from Pietrangelo found Bortuzzo in the middle of the ice. His wrist shot sailed just above the right leg pad of Gibson and into the net.