Gilbert threw to James Kirkendoll for a 63-yard TD early in the second quarter and connected with Malcolm Williams for a 47-yarder on the final play of the first half. Williams outjumped four Owls defenders to catch the ball in the end zone.
Acho's interception on the first play of the fourth quarter put Texas ahead 37-17.
Texas (5-6), which played for the national championship last season, must beat No. 18 Texas A&M on Thanksgiving night to become bowl eligible and avoid its first losing season since 1997.
Rob Housler had two touchdown catches for Florida Atlantic (4-6).
Texas coach Mack Brown hasn't had a losing season since 1989 at North Carolina.
The Longhorns hadn't won since Oct. 16 at Nebraska and had lost six of their last seven games -- struggles that led to tens of thousands of empty seats at kickoff.
But the Longhorns, who hadn't scored a first-half touchdown during their losing streak, hit the Owls for three in what was easily their best offensive performance of the season.
Texas had a season-high point total, more than doubling their average of 22. Kirkendoll's touchdown catch was the team's longest scoring play of the season.
Gilbert finished with 263 yards passing. Cody Johnson rushed for 124 yards and a TD, his third career 100-yard game.
It looked early like some of the same frustrating problems would hit Texas again when Johnson was stopped short of the goal line on fourth down on Texas' first drive. But Blake Gideon's interception two plays later gave Texas the ball on the 9, and Johnson scored on fourth-and-1 for a 7-0 lead.
The Owls struck back when quarterback Jeff Van Camp found Housler running by himself down the middle of the field. Housler had slipped behind safety Kenny Vaccaro and hauled in an easy 56-yard touchdown pass.
A fumble by Gilbert on the Texas 30 gave Florida Atlantic a chance to take the lead, but Ross Gornall's field goal attempt was blocked by Kheeston Randall. Gilbert then connected with Kirkendoll for a 14-7 Texas lead.
Gilbert and Williams teamed up for the highlight play of the Longhorns' long season.
Texas had the ball with four seconds left in the half. The Longhorns sent three receivers into the end zone and Gilbert launched a high pass that the 6-foot-3 Williams snared to make it 24-7.
Texas' Justin Tucker kicked two field goals and Housler hauled in his second touchdown catch for the Owls in the third quarter before Acho's play to start the fourth broke the game open.
Van Camp was under pressure when he floated a soft pass toward the sideline. Acho grabbed it and had a clear path to a touchdown.
Acho's TD was Texas' first defensive score since the first game of the season. Acho's brother, Sam, had three sacks.