VCU (39-23) advanced to a super regional against Miami or Columbia.
The Rams won three of four regional games, allowing only six runs.
Lees earned his third save, pitching 3 1/3 innings after relieving Thompson (6-3) in the sixth.
Joseph Shaw (10-5) lost to VCU for the second time in the tournament. He left in the second inning after forcing in a run by hitting James Bunn with a pitch and giving up another when Cody Acker grounded out.
Jimmy Kerrigan led off the sixth with a double, stole third base and scored on another groundout by Acker.
Plate umpire Barry Chambers was hit in the chest by a pitched ball, and was replaced in the seventh inning.
Dallas Baptist (46-15) had forced an extra game by edging VCU 2-1 earlier Monday. Closer Brandon Koch (3-2) pitched a season-high 4 2/3 innings, allowing two hits and striking out seven.
Daniel Sweet and Chane Lynch each singled to drive in a first-inning run. The loss ended the Rams' 13-game winning streak. But they won the deciding game.