Howard Payne (16-10) cut the Tech lead in half on Ryan Rodgers' solo home run in the third inning.
Alvarez gave Tech a 5-1 lead in the bottom of the third with a three-run homer over the left field wall. His blast was his seventh this season and extended his hitting streak to 18 games.
Later, after a run by Alvarez, Bryon Smith clubbed his fifth home run this season.
J.J. Newman (1-0) earned the victory, while Jesse Lopez (5-3) suffered the loss.
Tech returns to action on Friday night when they will host Kansas State at 7 p.m.