The Flames had led 1-0 for much of the game until the Oilers finally broke through with 10.1 seconds left in regulation when Taylor Hall scored off a pass from David Perron that was banked off Flames goalie Reto Berra.
But in the extra period, the Flames' Kris Russell sent a pass across the crease that Edmonton defender Justin Schultz fanned on, leaving it right on the stick of Hudler, who fired it into the open net.
Lee Stempniak scored in the first period and Berra stopped 30-of-31 shots for Calgary, which won for the third time in four games.
Devan Dubnyk made 25 saves for the Oilers, who were coming off an 8-2 win over Phoenix Thursday.
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