A 3-pointer by McDougald broke the game's 11th tie, giving the visiting Dolphins (10-10, 5-2) a 59-56 edge with 8 minutes left.
The Ospreys (8-12, 3-4) cut the lead to one point four times after that, getting to within 69-68 with 2:37 to play.
Glenn Powell, who scored 14 points for Jacksonville, responded with a jumper, and the Dolphins scored the game's final six points from the free-throw line.
Both teams shot well in the second half. Jacksonville made 60.9 percent (14 of 23) from the field and North Florida made 57.1 percent (16 of 28).
Parker Smith scored 19 points for the Ospreys, including 4 of 9 3-pointers. That matched his season average of 4.0 treys per game, tied for first in the nation.
NCAA title game hero Kris Jenkins said he will withdraw his name from the NBA draft and return to Villanova for his senior season.
Andy Katz breaks down the likelihood of Villanova, Syracuse, North Carolina or Oklahoma making a run to the Final Four next season.
Florida State has announced that Xavier Rathan-Mayes will return to the court for his junior season. The 6-foot-4 guard declared for the NBA draft last month but did not hire an agent.