Pominville notched his eighth and ninth goals of the season, including a shorthanded tally, as the Sabres and Devils battled to a 3-3 draw in regulation.
After a scoreless overtime, the game went to a shootout and Pominville went first, beating New Jersey's Johan Hedberg with a shot to the glove side.
Jochen Hecht also scored and Miller finished with 28 saves in the victory.
Henrique, Steve Bernier and Andrei Loktionov each found the net for New Jersey, which stumbled to its fourth straight loss and sixth in seven contests.
Hedberg ended with 20 saves for the Devils.