Trailing 24-22, Clemson took possession on its 20-yard line with 1:39 remaining. Quarterback Tajh Boyd completed a pass for 26 yards to DeAndre Hopkins on a fourth-and-16 play during the decisive 10-play drive.
Catanzaro's kick set off a wild celebration on the field and in the stands, while some players collapsed on the field in apparent disbelief.
In other bowl games on New Year's Eve, Southern California's disappointing season ended in fittingly downbeat fashion with a 21-7 loss to Georgia Tech in the Sun Bowl, Tulsa beat Iowa State 31-17 in the Liberty Bowl while Vanderbilt completed its best season in nearly a century by downing North Carolina State 38-24 in the Music City Bowl.
Quarterback Jeremy Hill ran for 124 yards and two touchdowns for LSU, which carried a 24-13 lead into the final quarter.
USC's season began with the Trojans holding the No. 1 ranking and with quarterback Matt Barkley as a strong contender for the Heisman Trophy, but he was on the sidelines with an injured shoulder as the season came to a drab end.
Georgia Tech quarterback Tevin Washington threw a touchdown pass and ran for another score to lead the Yellow Jackets to victory.
Washington's 1-yard touchdown run in the third made it 14-7, and he found Orwin Smith for a 17-yard touchdown pass in the fourth.
The Trojans struggled to contain Georgia Tech's triple-option attack. The Yellow Jackets rushed for 294 yards on 63 carries while stopping a seven-bowl losing streak.
In the Liberty Bowl, Tulsa avenged a season-opening loss to Iowa State by beating the Cyclones comfortably, with Trey Watts rushing for 149 yards and Alex Singleton running for three scores for the Golden Hurricane.
Tulsa trailed 17-7 at the end of the first quarter but came back to win and complete the second 11-win season in school history, with the other coming in 2008; an impressive feat for a college with the smallest enrollment of any Football Bowl Subdivision program.
Tulsa scored two touchdowns in the first four minutes of the second quarter to pull ahead for good.
Singleton's three scores gave him a school-record 24 touchdown runs this season.
The Commodores finished 9-4 for their best record since going 9-1 in 1915, and it's only the third time the smallest and only private university in the Southeastern Conference has won as many as nine games in a season. They also finished with seven straight wins, their longest streak since winning eight in 1948.
Vanderbilt forced a season-high five turnovers, including four in the first half, and turned those into 17 points.
N.C. State had its fifth game this season with at least four turnovers, wiping out a 424-225 advantage in yardage.