Omar Samhan scored 13 points to lead the Gaels (12-2), whose five-game winning streak ended.
Johnson, delivering the scoring muscle and shooting touch coach Rick Barnes promised he could, was 7-for-10 with a variety of layups, short jumpers and a powerful two-handed dunk in the second half that helped Texas put the game away.
A.J. Abrams and Damion James each scored 15 points for the Longhorns, who shot 53 percent. Abrams had his streak of 85 straight games snapped earlier in the week when he sat out Texas' win over TCU with a foot injury.
The Gaels hit nine 3-pointers but just one in the second half and shot just 36 percent from the floor. Saint Mary's was also 7-of-17 on free throws.
Saint Mary's led 29-24 before Texas took the lead behind two 3-pointers from Augustin and James, whose basket with 5:22 left in the half was his first in the game.
James hit another 3-pointer and Abrams made one from the left wing as Texas pushed its lead to 42-36 by halftime despite being outrebounded 25-13.
Johnson hit two strong baskets in the low post the early minutes of the second half, then stepped out for a soft mid-range jumper for a 50-42 Texas lead.
The Gaels got within three before Texas pushed the lead to 64-51 with a 14-4 run over the next four minutes. Abrams scored eight on a variety of slashing moves to the basket and pull-up jumpers.
Texas put it away with a pair of dunks. Johnson's was first after he powered past a defender with a strong move on the baseline. The next came on James' soaring, breakaway slam that put Texas up 70-64 with 9:32 left to play.
Texas built the lead to 21. The Gaels got within 15 in the final three minutes but could not stop Augustin's twisting, spinning drives through the lane for baskets or free throws.
Texas was outrebounded 41-34 but Johnson's muscle helped Texas hold the edge in scoring in the paint, 38-28.
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