Chris Knowlton and Scott Mayfield scored goals for the sixth-ranked Pioneers (9-4-2, 7-2-2 WCHA), whose winless streak reached five games.
Mayfield's goal at 7:43 of the second period gave Denver a 2-1 lead. But Corban Knight answered three minutes later for ninth-ranked North Dakota (7-5-3, 4-2-3) to tie the game.
Knight has scored points in 10 consecutive games. North Dakota has won six of the last nine games between the teams.
Denver led 1-0 after Knowlton's goal in the first period.
Carter Rowney tied the game early in the second.
North Dakota dominated in shots (33-20), but Denver sophomore goaltender Juho Olkinuora made 31 saves.
Clarke Saunders had 18 saves for UND.
The Pioneers play the second game of a back-to-back against North Dakota on Saturday at 6 p.m.
Denver senior Chris Knowlton has scored seven of his eight goals and has recorded four of his six assists in Saturday games.
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