Buffalo never led during the first 65 minutes of action and trailed 5-3 after Tomas Plekanec scored for Montreal 45 seconds into the third period.
Vanek brought Buffalo within one on the power play at the 8-minute mark of the third and his dramatic late goal ensured the Sabres at least a point.
Buffalo did better than that when Pominville tallied in the third round of the shootout to snap the Sabres' three-game losing streak.
Vanek, who has 10 goals for the season, also scored in the opening round. That goal was matched by one from Alex Galcheyuk.
Buffalo avenged a 6-1 loss to Montreal last weekend.