Wes Musick (2-0) gave up just one run on five hits over 6 2/3 innings for the Cougars (4-2). He struck out four and walked one.
A.J. Ramos (0-2) took the loss, surrendering three runs on three hits in 5 2/3 innings. Ramos walked four and struck out four.
Tully's solo home run to lead off the eighth gave the Cougars a 5-1 lead. But Joey Kenworthy and Roger Kieschnick of Texas Tech (2-4) both had RBI doubles in the bottom of the eighth to make the score 5-3.
Tully came on in the ninth with one man on and one out. He gave up back-to-back singles to load the bases before striking out Doug Thennis for the second out. Tully walked in a run before shutting the door with the groundout. He gave up no runs on two hits, striking out one and walking one.
Bryan Pounds had two RBIs for the Cougars, and Jake Stewart went 2-for-4 with an RBI.
Kenworthy went 2-for-4 and batted in two runs for Texas Tech.