Johnson's two-out double in the seventh broke open a close game. Smith's second RBI single the next inning gave reliever Nick Maronde a four-run cushion going into the ninth.
Randall (11-3) scattered five hits over 6.2 innings, walked none and struck out five. Only one of the four runs against him was earned. He retired 13 straight from the third to seventh innings.
Taylor Jungmann (13-3) had a third straight rough outing for the Longhorns, going 4.1 innings for his shortest start of the season.
Florida (51-17) moves to a Bracket 1 winners' game against Vanderbilt on Monday night. Texas (49-18) meets North Carolina in an elimination game that afternoon.