After losing six in a row, the Oilers have won their last two.
Smyth tallied with 2:38 left in the opening period and it remained a 1-0 game until he added an empty-net goal with only six seconds left in the contest.
Dubnyk protected the narrow lead and picked up the eighth shutout of his career. He has two shutouts in each of the last four seasons. The Edmonton netminder came into the game with a 3.38 goals-against average.
Reto Berra stopped 26 shots for Calgary, which has lost five of its last six.