The Bears opened the top of the third inning with three straight hits and extended their lead to 4-0 before Gooch retired the next three batters to end the inning.
Freshman right fielder Madison Edwards plated Tech's first run of the game with a solo blast in the bottom of the fourth to pull Tech (38-16, 14-11) within three at 4-1. Edwards' home run was the third of his career.
Later, senior Willie Durazo launched a solo home run in the sixth inning over the right-center field wall. The home run was his eighth this season and first since the Sam Houston State game on March 12.
Senior first baseman Austin Cranford got a two-run triple with one run in the bottom of the eighth to tie the game and later scored on pinch hitter Travis McElroy's first base groundout.
Baylor's Michael Griffin led off the top off the ninth with a triple, but Gooch was then replaced by Steve Rowe. Trey Webb then tied the game on a sacrifice fly to center field.
Mike Huggins kept the momentum going for the Bears in the 10th when he deposited a two-run home run over the right field wall to put Baylor ahead 7-5.
With the bases loaded and no outs in the bottom of the tenth inning, Tech responded with Jon Slack sacrifice, which scored Cranford and Scooter Jordan followed with a single to tie the game 7-7. Gera Alvarez delivered the game winning run with a sacrifice fly to center field that plated Bryon Smith from third.
Rowe picked up the win and improved to 8-2 this season, while Kyle Edens suffered the loss for Baylor and fell to 5-6.
Tech and Baylor will play the second game of the three-game series at 2 p.m. on Saturday afternoon at Dan Law Field.