Gainesville, FL (Sports Network) - Tim Tebow continued his march toward the Heisman Trophy, throwing for a career-high 338 yards and three touchdowns and also running for his 20th TD of the season, as 14th-ranked Florida cruised past Florida Atlantic, 59-20.

Tebow made history with his second quarter touchdown run, becoming the first player in NCAA history to throw for 20 touchdowns and also run for 20 TDs in the same season.

Tebow's main weapon through the air was wideout Andre Caldwell, who caught 13 passes for 164 yards to become Florida's all-time leader in receptions with 176. Kestahn Moore rushed for two scores while Cornelius Ingram caught two touchdown passes for the Gators (8-3), who have won four of five.

Rusty Smith threw for 290 yards and a touchdown and also ran for a score for the Owls (5-5), who made the game close in the second quarter before Florida closed the game out with 31 unanswered points. Receiver Cortez Gent ended with six catches for 118 yards and a touchdown.

Florida was all over Florida Atlantic in the first quarter, jumping out to a 21-0 lead.

The Owls reached Florida territory on the opening possession of the game, but the Gators forced a punt before marching 85 yards on just eight plays for the score. Caldwell's 22-yard reception set up Moore's touchdown run from nine yards out that gave Florida the lead.

The Gators defense followed with another stop and Joey Sorrentino came in untouched to block Mickey Groody's punt. Markus Manson picked up the loose ball and raced 19 yards to make it 14-0.

After a Florida Atlantic three-and-out, Florida then put together a 74-yard, nine-play drive that ended when Tebow found Ingram in the end zone on 3rd- and-goal from the four-yard line.

The Owls, however, finally came alive in the second quarter to make it a one- possession game.

Warley Leroy's 40-yard field goal early in the quarter got Florida Atlantic on the board before Corey Small stepped in front of a rare errant throw from Tebow. The Owls took over on the Florida 37-yard line and Smith soon hooked up with Gent for a 20-yard score that made it 21-10.

Florida Atlantic then forced the potent Florida offense into a three-and-out before Leroy's 43-yarder brought the Owls within 21-13 with just over seven minutes left in the half.

Tebow and Smith traded short touchdown runs, but it was the Gators carrying the momentum into halftime when Tebow once again connected with Ingram - this time for a 26-yard touchdown that made it 35-20 with just nine seconds left before halftime. A roughing-the-passer penalty on Florida Atlantic helped aid Florida's late scoring drive.

Louis Murphy gave the Gators good field position when he returned the opening second-half kickoff to the Florida 43-yard line. The Gators needed only four plays to score again as Moore crossed the goal line from six yards out for his second TD of the game that made it 42-20.

Florida Atlantic had a chance to answer, but on 4th-and-inches from the Florida 43-yard line, the Owls turned the ball over on a bad snap.

Tebow soon hooked up with Aaron Hernandez for his third TD pass of the game that effectively put the game out of reach.

In the fourth quarter, a 36-yard field goal by Joey Ijjas and a 24-yard Cameron Newton run capped the scoring.