Winston, who came into the game averaging nine points per game, scored in double-digits for the seventh consecutive game and eighth time in nine contests.
Portland State shot a season-high 61.4 percent (27 of 44) from the floor, recording 17 assists.
Winston's 3-pointer with 2:23 left gave the Vikings (11-8, 6-4 Big Sky) a 68-62 advantage. Troy Huff sandwiched a jumper and a layup around a missed 3-pointer by PSU's Tim Douglas, pulling North Dakota within two with 1:14 remaining.
DaShaun Wiggins pushed the lead to 70-66 with a jumper 25 seconds later before Jamal Webb's layup made it a two-point game with 43 seconds to go.
North Dakota forced a turnover but missed a 3-pointer at the buzzer.
Huff paced North Dakota (9-11, 6-4) with 20 points.
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