Bortles completed 20-of-31 passes for 301 yards and three touchdowns with two interceptions while rushing for 93 yards and a score on eight carries for the Knights (12-1), who made their first BCS bowl appearance thanks to an undefeated run in the American Athletic Conference.
"I think he came back and made some big plays with his legs and also turned some plays that could have been very bad for us, into really good plays getting the ball downfield," UCF head coach George O'Leary said of Bortles, who was named the game's offensive MVP.
Johnson racked up 124 yards on 20 carries and Rannell Hall hauled in a pair of touchdown passes in the win, UCF's ninth in a row since suffering its lone loss of the season against South Carolina on Sept. 28.
The Bears (11-2) notched their first-ever 11-win season, Big 12 championship and BCS bowl berth thanks in large part to the nation's top scoring offense during the regular season, but were unable to put up enough points to keep pace with the Knights despite a five-touchdown effort from Bryce Petty.
Petty rushed for three scores and tossed a pair of touchdown passes, finishing 30-of-47 passing for 356 yards with an interception in the setback.
"We caught a football team that was hot," Baylor coach Art Briles admitted. "They played extremely well early, got into us. We tried to play catch up the whole game, never could turn it around when it needed turning."
Petty's 1-yard TD run and subsequent two-point conversion scamper brought Baylor even at 28-28 less than five minutes into the third, but UCF found the end zone on each of its next three touches to take control of the contest.
The first score capped a 9-play, 76-yard trek that featured three third-down conversions, including a 3rd-and-4 from the Baylor 10 that saw Bortles hit Breshad Perriman in the back right corner of the end zone to put the Knights back on top.
Following a Baylor punt, Bortles broke free for 22 yards on the first play of the fourth quarter before scurrying into the end zone from 15 yards out two snaps later to make it 42-28 in favor of UCF.
Corey Coleman returned the ensuing kickoff 42 yards to help set up Glasco Martin's 9-yard TD run that brought Baylor within seven, but Johnson ripped off a 40-yard touchdown run four plays into UCF's next drive to restore the Knights' two-touchdown lead.
Shawn Moffitt nailed a 36-yard field goal on UCF's next touch and Petty hit Clay Fuller for a 9-yard touchdown with just over a minute left to account for the final margin.
Early on, Johnson found the end zone on UCF's first two touches, scoring from 11 yards out on the first drive and two yards out on the second to give UCF an early 14-point edge.
A short punt from UCF's Caleb Houston set the Bears up at the UCF 45 late in the first and after Lache Seastrunk converted a 3rd-and-2 with a 29-yard run to the 8-yard line, Petty scored from a yard out two plays later to get Baylor on the board.
Baylor's defense came up with a big play early in the second to help the team get within one, as Eddie Lackey picked off a Bortles pass at the UCF 32 and Petty hit Levi Norwood for a 30-yard score two plays later.
However, holder Brody Trahan dropped the snap on the ensuing extra point and tried to take off around the right end, but was tripped up short of the goal line, leaving Baylor trailing 14-13 with 8:01 left in the half.
After the teams exchanged turnovers, Bortles capped a quick 5-play sequence with a short screen pass out to the left for Hall, who followed his blockers and sprinted into the end zone for a 50-yard score and a 21-13 lead.
Petty answered with a 13-yard TD run that saw him leap for the right pylon and get flipped head-over-heels before landing on his back in the end zone to again bring Baylor within one.
UCF had the final say in the frame though, as Bortles went back to Hall on a short swing pass out to the right that Hall took the rest of the way for a 34- yard score that sent UCF into the break with a 28-20 lead.
UCF improved to 3-3 all-time in bowl games, while Baylor dropped to 10-10 ... UCF's 12 wins and nine-game win streak are both school records ... Seastrunk finished with 117 yards on 17 carries ... Hall had a game-high 113 receiving yards on four catches ... The teams combined for 1,106 total yards and 56 first downs ... Baylor was called for 17 penalties, totaling 135 yards ... Baylor set the all-time NCAA record for most points in a 13-game season with 681 points ... The 94 combined points were the most in Fiesta Bowl history and second most in BCS history behind the 2012 Sugar Bowl, which saw West Virginia and Clemson combine for 103 points.