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 school records for single-season rushing yards (1,697), single-season scoring (122 points), total touchdowns in a season (20), 100-yard rushing game in a season (9) and consecutive 100-yard rushing games (5).
"I can't even really put it into words," he said. "First of all winning and ... now that it's the end of the season and I found out I broke those records it feels good. I'm proud of myself and I'm proud of my teammates and coaches."
The Illini built a 24-0 lead and Leshoure's last touchdown put the game out of reach.
Illinois coach Ron Zook was informed late in the game that Leshoure needed 23 yards to set the rushing record.
"All we had to do was tell the offensive line and [quarterback] Nathan [Scheelhaase] that ... and they did the rest," Zook said.
Baylor's Robert Griffin III threw for 306 yards and a touchdown, but his two fumbles in the first half put the Bears behind.
Baylor coach Art Briles couldn't focus on the strides his team made this season in finishing with its first winning record since 1995.
"It's hard right now. It really is," he said. "Anytime you don't get the result that's desired, it doesn't feel good. It's a bad feeling. It's a bad feeling to have your face turned red."
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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. He kept the hat on when he spoke to reporters after the game.
"I like the hat," he said grinning. "It's my first cowboy hat. I'll use it as a souvenir and I might wear it out sometime."
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.
Illinois finished with 291 yards rushing and 533 yards of total offense to give Zook his first bowl win as a head coach in his fourth try.
"It's hard to win games and they're all big," Zook said. "I don't think there was a lot of people that gave us much of a chance in this game. So that competitor in you that wants to compete and if you can prove people wrong that's something you get satisfaction out of. That's not why you do it, though. I'm just happy for everybody."
Scheelhaase, a freshman, 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. His 13 completions were the most to start a game in school history.
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.
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 3 1/2 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.
"We had a good scheme coming in but they executed better than we did and that's why we didn't win the game," said Griffin, who set Baylor's career passing record with 6,073 yards.
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.
"We were very unstable early in the game," Briles said. "We let a good chance for momentum get away on the opening drive."
It was over when... The Fighting Illini rolled to a 24-0 lead, which proved to be more than enough against the Bears.
Gameball goes to... Mikel Leshoure, who torched the Baylor defense with 184 rushing yards and three touchdowns.
Stat of the game... 1. Ron Zook got his first bowl win as a head coach and the Illini won their first bowl since 1999.
Mikel Leshoure 13 Yd Run (Mikel Leshoure Run For Two-Point Conversion)
Jay Finley 4 Yd Run (Aaron Jones Kick)
Kendall Wright 39 Yd Pass From Robert Griffin III (Aaron Jones Kick)
Mikel Leshoure 5 Yd Run (Derek Dimke Kick)
Nathan Scheelhaase 55 Yd Run (Derek Dimke Kick)
Mikel LeShoure's 184 rushing yards against Baylor give him 1,697 for the season, the most by any player in a single-season in Illinois history. His 3 touchdowns tonight give him 17 rush TD on the season, tying Rashard Mendenhall for most in a single season in school history. This game marked his 9th 100-yd rushing game this season, also setting a school record.