Kansas (16-15, 3-10) scored five runs in the bottom of the third on four hits, a catcher's interference call and a hit-by-pitch.
Matt Harbin replaced starter Chris Phillips during the inning, which marked the shortest outing of his career.
Kansas added to its lead in the bottom of the fourth on a double by Ryan Baty, which plated Matt Tribble from first. Ryan Klocksien drove in Baty from second with a single to left center and Cole Armstrong busted it open with a two-RBI single, which gave the Jayhawks a 10-3 lead.
Phillips (4-3) suffered the loss, surrendering five earned runs on six hits in only two innings.
Jeff Davis (5-1) pitched his second straight complete game and earned the victory for Kansas.
Tech and Kansas will play the second game of the three-game series at 2 p.m. on Saturday at Hoglund Ballpark.