The jumped out to an early 14-point and kept rolling, piling up 556 total yards in the highest-scoring game in Fiesta Bowl history.
Rannell Hall had four catches for 113 yards and two touchdowns, and Johnson ran for 124 yards to give the Knights a rousing BCS bowl debut.
Baylor (11-2) had a hard time keeping up with the Knights, gaining 550 total yards but losing 135 on 17 penalties.
Bortles threw for three touchdowns on 20-of-31 passing and ran for another score.
Bryce Petty ran for three touchdowns and threw for 356 yards and two more scores for Baylor. Lache Seastrunk ran for 117 yards.
The Fiesta Bowl was the BCS coming-out party for Baylor and Central Florida before college football's switch to a playoff system next season.
The Bears had been building toward this since Art Briles became coach in 2009, winding up his high-octane offense to lead the nation in scoring and churn out the second-most yards in FBS history.
Central Florida had a slower rise under George O'Leary.
The coach who was fired by Notre Dame five days after being hired for lying on his resume has built his reputation back up in Orlando, taking a program that went winless in 2004 to the inaugural American Athletic Conference title and automatic BCS berth this year.
The matchup was projected to be like the 2011 Fiesta Bowl, when mighty Oklahoma rolled over Connecticut 48-20.
The Knights weren't listening.
They opened with a 76-yard scoring drive capped by Johnson's tackle-breaking 11-yard touchdown run. Johnson scored again on UCF's next possession, this one on a 2-yard run.
The early 14-0 lead was expected. The team leading wasn't.
Baylor finally revved up its offense late in the first quarter, scoring on a 1-yard TD sneak by Petty and Central Florida looked as if it was ready to fall apart with turnovers on three consecutive plays.
Baylor only turned one of those into points: a 30-yard from Petty to Levi Norwood. Petty followed Johnson's fumble with an interception in the end zone, just his third of the season.
Then came the spectacular plays, seemingly one after another.
Hall darted and dashed through Baylor's defense for a 50-yard touchdown on a screen pass, with help from Josh Reese's downfield block.
Petty hurtled himself into the end zone, flipping over UCF's Brandon Alexander to cap a 13-yard run. That gave Baylor 659 points, breaking the NCAA record for a 13-game season set by Texas (652) in 2005.
The momentum was gone shortly after, when Hall turned a swing pass into a 34-yard touchdown play assisted again by Reese to put the Knights up 28-20 at halftime.
Petty scored his third touchdown on 1-yard run in the third quarter and dashed in for the 2-point conversion to tie the game, but Central Florida still wouldn't back down.
Bortles hit Breshad Perriman on a 10-yard touchdown pass and opened the fourth quarter by scoring on an 11-yard run to put the Knights up 42-28.
Even after Baylor moved quickly for a 9-yard touchdown run by Glasco Martin, UCF had an answer, going up 49-35 on Johnson's 40-yard run through the heart of the Bears' defense.