The Wildcats (3-0) will play either Seton Hall or Saint Joseph's Sunday night for the title of the eight-team tournament.
Crawford hit his fifth 3-pointer with 5:06 left that put Northwestern in front 62-56. But the Golden Hurricane (3-1) got within 62-60 three minutes later on Jordan Clarkson's foul shots. That's when Shurna spun on defender Steven Idlet for a leaning basket and was fouled to extend the lead.
Tulsa cut it two on Clarkson's 3-pointer seconds later, but got no closer.
Shurna had 15 points.
Clarkson led Tulsa with 16 points.