Liberty, which won't be a full-time FBS school until 2019, rolled up 585 yards of offense and scored 31 points in the second half to pull off the upset. Flames quarterback Stephen Calvert passed for 447 yards, including a 26-yard, back-breaking touchdown to Spencer Jones, which put Liberty up 10 points with 6:12 to play.
Baylor had a chance at a Hail Mary in the final seconds, but the Flames intercepted the pass.
Liberty had never defeated a Big 12 school before and previously had only four wins over FBS opponents. Baylor's only previous loss to a lower-level team came in 1981 to Lamar.
According to FPI, Liberty had a 2.2 percent chance of beating Baylor, making it the second-biggest FPI upset in the past 10 years. The only bigger upset was Howard's 43-40 stunner over UNLV later Saturday. Howard, a 45-point underdog, had a 1.2 percent chance to win, according to FPI.
Rhule arrived from Temple last December in the wake of a sexual assault scandal at Baylor that led to the firing of coach Art Briles. Jim Grobe coached the Bears on an interim basis last season. Hiring Grobe was one of the last moves made by Liberty athletic director Ian McCaw, who resigned as athletic director at Baylor shortly after a report alleged that the school mishandled sexual assault cases involving football players.
Baylor's start to the season got worse when starting running back JaMycal Hasty had to leave the game with a knee injury that Rhule said could keep him out for a month. The Bears were already without 1,000-yard rusher Terence Williams, who himself is expected to be out another month with a shoulder injury. Without Hasty and Williams, the Bears will be forced to rely on true freshman John Lovett, who rushed for 89 yards and two touchdowns on Saturday.
ESPN Stats & Info and The Associated Press contributed to this report