The Pirates (36-21) trailed 6-3 entering the bottom of the ninth. Facing Cavs closer Tommy Doyle (2-6, 5.75 ERA), who had posted a 1.20 ERA in 14 innings since being moved to the bullpen last month, Kirk Morgan led off with a pinch-hit single.
Parker Lamm followed with an RBI double that scored pinch-runner Wesley Phillips from first to make it 6-4 UVA.
Charlie Yorgen lined a single to right to plate Lamm and make it 6-5.
Dwayna Williams-Sutton singled, and Turner Brown sacrificed the runners to second and third.
Watkins, 0-for-4 on the day to that point, blasted a 1-1 fastball to left-center into the far reaches of the Hoo Zone to send the Pirates to the regional final.
UVA (38-21) will face William & Mary (30-30) in an elimination game Sunday morning. The Tribe eliminated Bryant (47-12) with a 4-3 win earlier Saturday.
Virginia starter Connor Jones had efforted his way through five and a third tough innings, allowing three runs, two earned, on nine hits, walking one, hitting two ECU batters and striking out three.
East Carolina was 0-for-12 with runners in scoring position against Jones, though, and left eight runners on base.
Pavin Smith homered twice for Virginia. Ernie Clement was 3-for-5 at the plate, and Matt Thaiss was 1-for-4 with a two-run double in a four-run UVA third.
Yorgen was 4-for-5 for East Carolina, and Garrett Brooks was 3-for-4 for ECU, which had 15 hits on the day.