Khabibulin stopped 21 shots in the second period alone as the Oilers were notching a pair of goals to break the contest open.
The shutout was the first of the season and the 46th in the career of the 40-year-old netminder, who improved to 3-3-1 on the season with the victory.
Jake Allen was pulled in the second period after yielding three goals on just seven shots for the Blues, who hold the seventh seed in the West.
Jaroslav Halak relieved and made 12-of-12 stops the rest of the way.
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