Texas Tech led 35-31 at halftime and had its lead trimmed to one early in the second half.
But the Red Raiders cinched things with a 17-3 run to put the game away in their season opener.
The win gives Texas Tech's Bob Knight, who became the all-time winningest coach in Division I men's basketball history last season, his 891st career win.
The Highlanders got within 45-44 on Sean Cunnigham's jumper with 13:12 left.
Voskuil, who scored 12 points, answered with a layup and a 3-pointer to put the Red Raiders up 50-44. That started the game-winning spurt, which ended with Texas Tech ahead 62-47.
Voskuil also had four steals as UC Riverside turned the ball over 27 times.