Hundley threw for 281 yards and two touchdowns and also ran for two scores as the Bruins (4-1, 1-1 Pac-12) improved to 30-10-2 in the weeks following a loss that dropped them from the rankings. They tumbled from No. 19 last week with a loss at home to Oregon State.
Franklin set the tone early, running for 97 of his 111 yards in the first half and catching all three of his passes for 48 yards as the Bruins jumped ahead 21-7 at the break.
The Buffaloes (1-4, 1-1) were driving in the third quarter when they were stuffed on fourth-and-1 at midfield, then coughed up the ball on their next two possessions.
"We're not at that point where we can overcome mistakes like that," Buffs coach Jon Embree said.
The Buffaloes rallied past Washington State last week with three touchdowns in the final seven minutes, and they needed a similar comeback this time after falling behind by three TDs through three quarters.
It was the Bruins who poured on the points this time, sealing their first win in Boulder since a 33-16 victory in 1984. They returned in 2003, losing 16-14.
Franklin, who was limited to 45 yards a week earlier, had a big first half, when his 28-yard bob-and-weave on a screen pass set up Hundley's 1-yard TD keeper that put UCLA ahead 21-7 at halftime.
UCLA linebacker Eric Kendricks and free safety Tevin McDonald had a monster second half, teaming up to stuff Tony Jones on fourth-and-1 at midfield in the third quarter when the Buffs had the momentum and still harbored hopes of an upset, then combining for a crucial takeaway on their next series.
McDonald punched the ball free after tight end Vincent Hobbs hauled in a long pass and Kendricks scooped it up.
The Bruins poured it on from there, starting with Hundley's 8-yard TD pass to Joseph Fauria that made it 28-7. Safety Stan McKay picked off a pass from Webb at midfield and returned it to the Colorado 35, setting up a 25-yard TD run by Franklin's backup, Jordon James.
Franklin was the lead blocker on running back Damien Thigpen's 23-yard touchdown on a reverse that made it 42-7.
The Buffaloes gained just 35 yards in their first four possessions before Webb threw a 17-yard scoring strike to Dustin Ebner, the senior's first career touchdown. Nick Hirschman threw Colorado's other TD pass, a 31-yarder to tight end Nick Kasa in the waning minutes of the fourth quarter.
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