Javi Herrera, who went 4-for-5, keyed the ninth inning spurt with a two-out single before Cleveland belted his third home run of the season to left. He also added a sacrifice fly in the third.
The loss was Tennessee's seventh in its last eight games as it fell to 11-8. Purdue improved to 8-4 as Dustin Glant (1-0) earned the victory in two innings of relief.
The Boilermakers got two quick singles off Steve Wesley (0-1) to start the 10th as Underwood took third following Simon Klink's hit to right. Luke Hochevar replaced Wesley and promptly gave up a deep fly ball to Manuel that scored Underwood with the winning run. Hochevar retired the next two hitters on a strikeout and a fly out.
Purdue made short work of Vol starter Joey Andrews, who was tagged with four runs in 1 1/3 innings. They jumped out to a 1-0 lead in the first as Andy Rempel roped a double off the left field wall, took third on an error and scored on sacrifice fly.
The lead was extended to 4-0 in the second as they loaded the bases on three hits before plating runs on a hit batter, a walk and a sacrifice fly.
Walter Sevilla's sacrifice fly got Tennessee on the board in the bottom of the second.
A lead-off walk issued by Patrick Green to Simon Klink cost the Vols a run in the third as he scored on Eric Wolfe's single to center after moving to second on a sacrifice hit. That would be all they would get as the Vol bullpen shut down the Boilermakers over the next six innings.
Rob Fitzgerald kept Purdue in check for three innings as he retired nine straight after giving up two singles in the sixth.
Tennessee hosts the No. 10 South Carolina Gamecocks Friday at 7, Saturday at 7 and Sunday at 2. Saturday's game will be televised live by Comcast Sports Southeast.