From Roll, Bama, Roll’s great writeup on the 1960 Bluebonnet Bowl between the Alabama Crimson Tide and the Texas Longhorns: “More than 68,000 fans gathered under sunny skies and slightly chilly temperatures in Rice Stadium on Dec. 17 (1960) to see the bowl rematch between the two programs. Once again, it was a battle of defenses with both teams struggling for whatever points they could get.”
They got very little. The game ended in a 3-3 tie. You can read more about i here.