Jordon James rushed for 155 yards and a touchdown, and Phillip Ruhl returned a blocked punt for a short touchdown as UCLA thoroughly spoiled the debut of Nevada coach Brian Polian with a 41-point second half.
Cody Fajardo passed for 164 yards and rushed for two TDs, but the Wolf Pack couldn't keep up in their debut under Polian, the 38-year-old picked to replace Hall of Fame coach Chris Ault.
Hundley went 22 for 33 in an impressive follow-up to his record-setting freshman campaign, rushing for a 37-yard TD on UCLA's opening drive and adding another TD run to open the second half.
Hundley also had plenty of help from a dominant offensive line and a running game that racked up 345 yards.
James looked sharp in his first game as the Bruins' starting tailback, but UCLA auditioned several ball-carriers for the chance to replace Johnathan Franklin, the school's departed career rushing leader known as Jet Ski.
The Bruins never punted on a warm night at the Rose Bowl, and they scored on each of their first five drives in the second half in the schools' first meeting.
Polian, the former Stanford and Texas A&M assistant coach, had little luck stopping UCLA's potent offense in his first game since replacing Ault, the architect of the pistol offense during 28 seasons. The Wolf Pack have made eight consecutive bowl appearances.
Fajardo, an Orange County native, went 19 for 32 and rushed for 106 yards on an otherwise rough night in front of several dozen friends and family members. A big chunk of Nevada's roster is from Southern California, including all three of Fajardo's starting receivers.
After the Bruins stopped Nevada's opening drive, Hundley showed his playmaking skills haven't faded since he set a single-season school record for total offense last year. After leading the Bruins past midfield, he made an impressive ball fake and rumbled up the middle for a score.
Hundley made a long TD run on UCLA's opening drive for the second straight season, even if it wasn't as long as his 72-yard rumble on his first collegiate snap as a freshman last year.
Hundley showed off his improved arm strength on a series of big throws, but didn't get many chances in the first half while Nevada controlled the ball for 18 1/2 minutes.
Fajardo matched Hundley early on, engineering a series of long drives that were undone near the goal line by penalties or small mistakes.
The Wolf Pack persevered with two field goals, followed by Fajardo's leaping, lunging TD at the corner of the end zone with 7 seconds left to trim UCLA's halftime lead to 17-13.
But Hundley led another scoring drive right after halftime, following guard Xavier Su'a-Filo right into the end zone for his second score.
Ruhl, the Bruins' fullback, then picked up a fortunate bounce when Kenny Orjioke blocked a punt by Nevada's Chase Tenpenny, who had to field a bouncing snap. The ball ricocheted high into the end zone and then bounced straight to Ruhl, who dived over the goal line.
UCLA took control from there, scoring on its first five drives after halftime.
Bruins freshman defensive back Justin Combs, the son of music mogul Diddy, made his first career tackle in the fourth quarter.