Halstead struck out three and walked three in shutting down the high powered Vol attach.
Tennessee manufacture their only run of the game in the first inning as center fielder Jordan Czarniecki was hit by a pitch, advanced to second on a groundout, stole third and then came home on another groundout.
WVU tied the game in the fourth on a Kurtis Clinton solo home run, then took the lead on Grant Psomas' RBI double, which drove home Tim McCabe.
The Mountaineers added another run in the fifth on a Lee Fritz sacrifice fly.
Tennessee put runners in scoring position in the fifth, sixth and seventh innings, but each time Halstead was able to work his way out of trouble.
WVU, which evened their record at 3-3, faces the Volunteers again at 2:00 p.m. on Sunday.