After a scoreless overtime, the game moved to shootout.
Colborne bested Elliott on a wrist shot on the first try of the tiebreaker and Reto Berra preserved the win by stopping Magnus Paajarvi on the Blues' final attempt.
Hudler and Mike Cammalleri each notched a goal and an assist as Calgary broke a four-game losing streak.
Berra finished with 32 saves.
Paajarvi, Jaden Schwartz and Kevin Shattenkirk scored for the Blues.
Elliott stopped 23-of-26 shots.
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