McClain, a senior out of Knoxville, got all the support he would need in the bottom of the first as catcher Michael Wheeler lined a two-run triple off the wall in right center field.
Brian Lucas followed with a sacrifice fly for a 3-0 lead and it was off the the races for McClain.
McClain struck out nine Trojans, walked two and recorded six putouts of his own to improve to 7-2 on the season.
"Lance is a very cool customer," said CU coach Woody Hunt, "he had a dominating change-up tonight. He gives up a lot of confidence. This was a big step toward us getting back to Lebanon next week."
All-conference outfielder Nick Jiles had a pair of hits for the winners while Wheeler added an RBI single in the fifth in addition to his triple. The former JUCO All-American has six RBI in two tournament games.
Trevecca dropped to 34-13 and will face a 12 Noon elimination game Wednesday against Union University.
The NAIA Region XI tournament will be held at CU's Stockton Field next week. Trevecca and Lambuth have already secured berths. Cumberland must finish at least third this week in order to qualify for the six-team double-elimination tournament.