Tennessee (22-12), which never led in the first 16-plus minutes of regulation, will next head to Raleigh for a date with Massachusetts, the No. 6 seed in the Midwest Region.
Josh Richardson scored 17 points -- all after halftime -- and helped hold Iowa's leading scorer, Roy Devyn Marble, to seven points on 3-of-15 shooting.
Marble sent the game to overtime with a late jumper, but finished 10 points below his season average. Adam Woodbury stepped up with 16 points and eight boards in the loss.
Iowa's final game epitomized its season, as the Hawkeyes (20-13) started out strong and ultimately fell flat as they missed all eight of their shots in overtime to lose for the seventh time in their last eight games.