The Fighting Irish's third leading scorer behind stars Matt Carroll and Thomas, Miller made just one of his first 12 shots before coming up with the game's biggest basket.
Thomas found Miller, who fought his way inside, and banked his shot in to give the Irish a 56-55 lead. Just 16 seconds earlier, 6-10 freshman Kevin Pittsnogle stepped outside and drilled a 3-pointer to give the Mountaineers their first lead of the contest.
Following a timeout, West Virginia went to Drew Schifino, who missed a tough runner. Miller followed by missing the front end of a 1-and-1 with 5.2 seconds left, leaving the door open for the Mountaineers.
But instead of using a timeout, the Mountaineers rushed the ball up court and Schifino missed an off-balance 3-pointer off the back of the rim as time expired.
Carroll scored 16 points and Thomas 10 of his 13 in the second half for Notre Dame (20-5, 8-3 Big East West), which reached the 20-win mark for the fourth straight season. The Fighting Irish also beat West Virginia for the eighth straight time.
Schifino finished with 19 points for the Mountaineers (13-10, 4-7), who rallied from a 15-point second-half deficit.