All three of St Croix's goals came on the power play and it was the fourth time he has recorded a hat trick in his WHL career.
Travis Ewanyk and Curtis Lazar had the other goals for the Oil Kings (6-3-3).
Brayden Point, who entered the contest second in rookie scoring with three goals and nine points, had the lone goal for the Warriors (5-5-1).
Tristan Jarry turned aside 23 shots for the win as Daniel Wapple stopped 28-of-33 shots before being replaced at the start of the third period by Justin Paulic, who saved two shots in relief.
Lazar opened up the scoring 3:43 into the game, backhanding a rebound past Wapple.
Point tied the game up for Moose Jaw five minutes later, after eluding defender Keegan Lowe and sliding the puck behind Jarry.
Edmonton's third-ranked power play went to work when St. Croix scored on a one-timer from the high slot at 12:12.
Ewanyk doubled the margin with just under three minutes to go in the first, after jamming in a rebound off Wapple's right pad.
St. Croix replicated his first power-play goal with another at 11:43 of the second to put Edmonton up by three.
He then buried his hat-trick goal 4:36 later as he tucked home a rebound off Wapple's left pad.
Edmonton went 3-for-5 on the power play while Moose Jaw failed to score on six chances with the man advantage.