Kansas State (13-9, 4-7), which saw head coach Jim Wooldridge return to the bench just a week after neck surgery, hit four of its first six shots and led 9-7 in the early going.
But the Wildcats were unable to get the lid off the basket for the next eight minutes as Texas Tech used a 14-0 run to build a 21-9 lead midway through the first half.
The Red Raiders stretched their advantage to 34-20 at the break, then scored 10 of the first 13 points of the second half to lead 44-24 with just over 15 minutes to go.
Tech's lead would reach as many as 27 points on two occasions over the final 10 minutes before K-State began chipping away.
A 3-pointer by Voskuil with 2:06 to go put the Red Raiders up 70-45 before the Wildcats scored the final 11 points of the game to close the gap.
Kansas State returns to action on Saturday, Feb. 18, at 12:30 p.m. when the Wildcats host Colorado at Bramlage Coliseum. The game will be televised in the Big 12 region on ESPN Plus.