The freshman from Garland, Texas, made the most of his collegiate debut, pouring in 14 points to go along with five rebounds and three assists.
Four Texas Tech players joined Smith in double-figure scoring. Tommy Hamilton IV and Keenan Evans each tallied 12 points, while Davide Moretti added 10 points.
Jordan Andews posted 15 points to pace South Alabama (0-1), which shot 30.4 percent. Herb McGee added 11 points for South Alabama.
The Red Raiders pulled down 40 rebounds and recorded 11 steals. Texas Tech saw 12 players grab a rebound.
Brandone Francis led Texas Tech with six rebounds, tying South Alabama's Trhae Mitchell for the game-high. Hamilton IV and Zach Smith (no relation to Zhaire) snared four boards apiece.
The Horned Frogs made the most of those steals with 27 points off of 24 Jaguar turnovers.
Texas Tech shot 49 percent from the field, but hit on just 25 percent of its 3-point attempts (5 of 20).