Goaltender Matt Murray made 34 saves and turned aside two skaters in the shootout to earn the win. Joel Vienneau stopped 32 shots for Sudbury.
The Greyhounds needed a last-minute goal from Miller to tie the game and send it to overtime.
Schiller's goal also marked the rookie forward's first OHL point.
Defenceman Ryan Spoul set up a pair of goals for the Greyhounds, giving the veteran six points in four games since returning from injury where he missed 16 games.
The Greyhounds scored once in two power-play attempts while the Wolves were 1-for-3 on the man advantage.