UNC Asheville (13-11, 7-3 Big South) shot 48 percent, including 9 of 20 beyond the arc, and has won three in a row.
Liberty (9-16, 3-7) has dropped four straight.
Asheville raced out to a 10-point lead through the first five minutes and led 47-34 at the break after Rowsey drilled a trey with 6 seconds before halftime.
Liberty kept chipping away at the lead after the break, finally taking the lead at 58-57 with 9:06 left on an Antwan Burrus layup. Rowsey's layup tied the game at 69 with 1:10 remaining, and Asheville hit its last five free throws to seal the win.
Liberty turned the ball over four times, fouled six times -- including a technical, and missed its last two shots in the last 1:30.