Schmaltz's backhand shot from in front of the net slipped past goalie Tanner Jaillet, setting off a wild celebration among Fighting Hawks fans in the crowd of 18,037 at Amalie Arena.
Drake Caggiula scored a pair of second-period goals for North Dakota. Rhett Gardner added an empty-netter with 1.9 seconds remaining.
North Dakota's trip to the Frozen Four in its first season under coach Brad Berry is the 22nd for the Fighting Hawks. They will face No. 1 overall seed Quinnipiac on Saturday night in the title game.
Quinnipiac (32-3-7) advanced with a 3-2 victory over Boston College and is looking for its first national title. North Dakota (33-6-4) has won seven NCAA crowns, tied with Denver for second behind Michigan's nine.