The Bears' senior quarterback also scored on a 1-yard keeper in the fourth quarter following a 42-yard interception return by safety Mike Lowe.
The ending was in sharp contrast to the opening drive for UCLA.
The Bruins got creative when Hundley threw a 4-yard touchdown pass to Cassius Marsh, a defensive end who lined up on the left side of the offensive line then ran a short out pattern. It's a formation UCLA has used previously this season, but the first time Marsh, a 275-pound senior, has scored.
Cal responded with a 26-yard field goal by Vicenzo D'Amato then took the lead on Maynard's 9-yard touchdown pass to C.J. Anderson midway through the second quarter.
Maynard got the drive started with a 42-yard completion to tight end Richard Rodgers then capped it with the throw to Anderson, who beat safety Tevin McDonald on an slant pattern.
That came after Hundley was charged with a fumble after his short pass in the left flat to Jordan James was ruled a lateral and recovered by Cal's Nick Forbes.
After UCLA kicker Ka'imi Fairbairn missed a 46-yard field goal attempt, the Bruins forced a punt but Kenny Orjioke ran into return man Steven Manfro as Manfro was calling for a fair catch. The ball hit Orjioke in the back and Cal pounced on it.
Five plays later, Maynard connected with Keenan Allen for an 8-yard touchdown on an inside slant play similar to the one run by Anderson.
The Bruins committed their third turnover of the first half when Hundley threw an interception in the end zone after the intended receiver stopped his route well short of the goal line.
Maynard threw touchdowns on Cal's first two drives in the second half to push the lead to 29-14.
UCLA pulled within 29-17 on Fairbairn's 30-yard field goal early in the fourth quarter, but Cal's defense came up with two more interceptions to secure the win.
"They were relentless," Mora said of the Bears. "They were maniacal. They did bring a lot of pressure and we've got to learn to handle that better."
Rodgers caught seven passes for 129 yards for Cal while Allen caught a pair of touchdowns and finished with eight receptions to move into third place on the Bears career list.
Anderson rushed for 151 yards, 68 on a touchdown run in the fourth quarter to extend Cal's lead to 26 points.