The Illini spoiled the Bears' first bowl appearance in 16 seasons. Both teams finished at 7-6.
Leshoure had a 5-yard TD run in the second quarter, a 13-yard score in the third quarter and another 5-yard touchdown run in the fourth period. The performance gave him the school single-season rushing record with 1,697 yards.
The Illini built a 24-0 lead and Leshoure's last touchdown put the game out of reach.
Baylor's Robert Griffin III threw for 306 yards and a touchdown, but his two fumbles in the first half put the Bears behind.
Leshoure was chosen the most valuable player and wore a cowboy hat as he hoisted the trophy above his head after the game while the small but vocal group of Illinois fans cheered.
The Bears cut the lead to 24-14 when Griffin found a diving Kendall Wright on a 39-yard touchdown pass on fourth-and-14 early in the fourth quarter. But Illinois continued its dominance in the rushing game after that and extended its lead to 31-14 on Leshoure's last touchdown.
Illinois finished with 291 yards rushing and 533 yards of total offense to give coach Ron Zook his first bowl win as a head coach in his fourth try.
Freshman quarterback Nathan Scheelhaase got off to a sensational start, completing all of his 13 passes in the first half, and finished 18 of 23 for 242 yards. He scored on a 55-yard touchdown run with 41 seconds to play to make it 38-14.
Illinois opened the second half with an 87-yard drive capped by a 13-yard touchdown run by Leshoure. Leshoure also scored the 2-point conversion to extend the lead to 24-0 and set the Illinois single-season scoring record.
Baylor finally found its offensive touch on its first possession of the second half. Griffin completed five of seven passes on that drive, which ended with a 4-yard touchdown run by Jay Finley to get the Bears within 24-7 with about eight minutes remaining in the third quarter.
The Illini held Finley in check for most of the night and Baylor's 1,000-yard rusher finished with 12 carries for 63 yards.
Illinois led 9-0 before a 5-yard touchdown run by Leshoure about 10 minutes before halftime stretched the lead to 16-0. That score was set up by a 52-yard reception by Ryan Lankford a play earlier.
Baylor was driving with about 3½ minutes left in the first half when a pass by Griffin was intercepted by Terry Hawthorne. But the Bears got a second chance when Corey Liuget was penalized for roughing the passer, giving Baylor the ball back.
The Bears still came away empty though when Griffin fumbled a few plays later to give Illinois the ball back on its own 32.
Baylor's problems started early with Griffin fumbling on the first possession. Travon Bellamy recovered that fumble and returned it 46 yards. The Illini couldn't get anything going on that drive and settled for a 38-yard field goal to take a 3-0 lead.
Illinois added a second field goal on their next drive to push the lead to 6-0 and a third field goal early in the second quarter made it 9-0.