Snyder blasted the only home run of the game for the Cougars, who snapped a four-game losing streak to the Bears and improved to 1-0 for the first time since 1999.
The Cougars continue their run in the tournament when they face No. 9 Texas at 7:30 p.m. Saturday.
Cougar reliever Jesse Crain collected the win after striking out the only batter he faced. In the top of the ninth, Crain moved onto the mound from his starting shortstop position and struck out Trey Webb with the go-ahead run on third base.
UH reliever Nathan Mitchell also provided a spark for the Cougars out of the bullpen. After entering the game in the sixth inning with the score tied at 2-2 and runners on second and third, Mitchell struck out Josh Ford and then threw 2.2 more innings of shutout, two-hit relief to set the stage for Snyder's heroics.
The Cougars struck for the game's first run in their first at-bat of the season. After outfielder Michael Bourn led off with a double, designated hitter Keith Whatley plated him with a single through the right side for a 1-0 UH lead.
That came after Cougar starter Brad Sullivan pitched his way out of a jam in the first inning. Tim Hartshorn led off with a triple down the right field but would get no further after Sullivan struck out the next three batters. The UH righthander would go on to tie a career best with nine strikeouts in 5.1 innings.
UH added to its lead in the second inning. Crain led off with a single to center and moved to third on a two-base error by the Baylor outfield before scoring on Thanos Papavasiliou's RBI-groundout.
Baylor tied the score in the sixth inning with a pair of unearned runs. After walks to Hartshorn and Chris Durbin, Hartshorn was plated on a two-out Cougar throwing error in the infield. Pinch-hitter Jared Clements then laced a double off the leg of UH reliever Danny Zell to plate Durbin and tie the score at 2-2.