Utah's Nick Schmaltz tied the game with a power-play goal at 9:17 of the middle frame with a shot from the doorstep.
Lawson Crouse gave the Mammoth a 2-1 lead with a one-timer from the right circle at 12:30 of the second period.
Drury tied the game at 1:10 of the third period with his first goal of the season via a shot from the left doorstep set up by Ross Colton's saucer pass.