Brendan Walker had the other tally for Saskatoon (44-22-4) and netminder Andrey Makarov made 39 saves in goal.
The Blades have posted an impressive 21-1-1 record in their last 23 games, including an 18-game winning streak, to climb their way from seventh place to second in the WHL's Eastern Conference.
Keegan Lowe and Dylan Wruck had the goals for Edmonton (49-15-6), while netminder Laurent Brossoit turned aside 35 shots.
McColgan was the only player to score in the shootout, backhanding the puck five-hole behind Brossoit.
Lowe opened up scoring at 11:02 of the first period for Edmonton, finishing off a 2-on-2 with Wruck as he slipped the puck past Makarov.
Saskatoon had the better of the chances early in the second period, making stacked-pad saves on both Lukas Sutter and Darren Dietz. But it was Wruck with the only goal in the middle stanza to make it 2-0 Edmonton, jumping on a rebound to lift the backhand up and over Makarov's left pad.
Blades' captain Walker continued his hot play in March, putting Saskatoon on the board at 4:13 of the third with a labelled wrist shot off the post and in behind Brossoit. The tally was Walker's fifth goal and 10th point in the past six games.
McColgan knotted the game up at two apiece at 8:31. He was left unchecked to stretch out and knock home a rebound off Brossoit's left pad, forcing extra time.