The Tigers (4-4, 2-3 Big 12), who scored two touchdowns in the fourth quarter, then held Texas A&M (5-3, 3-2) to four plays on their subsequent possession to secure the win.
Franklin finished the day 16-of-24 for 198 yards and two touchdowns. Henry Josey ran the ball 20 times for 162 yards and a score.
Ryan Tennehill had a banner day in the air, completing 35-of-53 passes for 317 yards and a trio of TDs.
The Aggies jumped to a 28-17 lead at halftime but were held to a field goal in the second half.