Barnes is the 13th active major college coach to reach the 600-victory mark and did it in his 28th season, his 17th with the Longhorns. Texas (16-8, 5-6 Big 12) also won its second consecutive game after a four-game losing streak.
Felix made four of Texas' seven 3-pointers. Cam Ridley added 15 points and 12 rebounds for the Longhorns.
Kyan Anderson had 11 points for TCU (14-10, 1-10), which scored just 16 in the first half in dropping its seventh straight loss.