Johnathan Franklin rushed for 217 yards and caught an 8-yard TD pass with 2:13 to play for the Bruins, who improved to 2-0 under new coach Jim Mora with an impressive offensive performance against the Cornhuskers (1-1).
After Jones' ferocious sack put the Bruins ahead in a defense-dominated second half, Andrew Abbott intercepted a long pass by Martinez and returned it to the Nebraska 16, setting up Franklin's TD catch.
Martinez passed for 179 yards and made a 92-yard TD run in his return to his native Southern California.
Ameer Abdullah rushed for 119 yards and two touchdowns for the Huskers, who struggled on both sides of the ball in the second half.
Martinez went 17 for 31, but just 4 for 14 after halftime on the field where the Corona, Calif., native always imagined playing for the Bruins, who only recruited him as a safety and never offered him a scholarship.
After a tentative third quarter for both teams, UCLA got a break when Jones somehow was left unblocked on Nebraska's first snap after a punt from its own 5, emphatically sacking Martinez. Franklin broke a 54-yard run moments later for the Bruins, but they missed a field goal with 6:49 left.
After Abbott's interception on a poorly thrown ball and Franklin's TD, Brett Maher's third field goal pulled the Huskers within 36-30 with 1:38 left. But UCLA recovered the onside kick and ran out the clock on just its second win over Nebraska in eight meetings since 1973.
The Bruins were undeniably impressive in the home debut of Mora, the veteran NFL coach who took over for Rick Neuheisel last winter after four mostly dismal seasons. Mora arrived with no significant college experience, but the former Falcons and Seahawks coach immediately energized UCLA by hiring a strong staff and landing an impressive recruiting class.
With this effort against a perennial national power, the excitement in Westwood will only grow.
UCLA has topped 640 yards of offense in each of its first two games under new offensive coordinator Noel Mazzone, the former Arizona State coordinator. Hundley, who rushed for a 72-yard TD on his first collegiate snap last week, repeatedly targeted Fauria, his 6-foot-7 tight end, and hit freshman Devin Lucien three times for 70 yards.
Blue-clad Bruins fans might have barely outnumbered an enormous contingent of red-wearing Huskers supporters who filled the Rose Bowl parking lots hours before kickoff and raised chants of "Go Big Red!" in the stadium. Eight Nebraska players are from Southern California.
Nebraska made its first visit to the Rose Bowl since losing the 2002 BCS title game to Miami, and the Huskers came into Pasadena hoping to return on New Year's Day as the Big Ten's representative.
Both offenses moved easily in the 24-24 first half, combining for 705 yards. Manfro's 49-yard TD catch-and-run put the Bruins ahead late, but Maher's 54-yard field goal at the gun evened the halftime score at 24.
Both teams made significant mistakes in the third quarter, with Nebraska fumbling on its first play and UCLA later failing on a fake field goal from 37 yards. When Hundley left the game for a few plays to get his right ankle re-taped, the Bruins had to settle for a field goal inside the Nebraska 5.
The Huskers didn't convert a third down until the first play of the fourth quarter, but Maher barely missed a go-ahead, 37-yard field goal with 12:12 to play.