No. 3 national seed Florida (50-19) will play No. 4 seed LSU (52-18) in the best-of-three finals beginning Monday night.
Daniel Murphy had four RBIs for the Nationals.
The Tigers (52-18) won their third straight elimination game, including back-to-back victories over Oregon State.
Anthony Rendon and Daniel Murphy also homered for the Nationals, who trailed 5-2 in the sixth before coming back to deal the Reds their 12th loss in 13 games.
The teams will meet again Saturday, with the winner going to the best-of-three finals beginning Monday.