But senior point guard Patrick Rembert was trapped along the sideline in front of his own bench on UCI's subsequent possession and his pass to Chris McNealy near the baseline was too late for McNealy to get a shot off before the buzzer sounded.
UCLA's 74-73 triumph upped its record to 8-4 and prompted a sigh of relief from many of the 6,830 in attendance.
UCI (6-6) had six possessions with a strong chance to score before the final fateful sequence. But each time, either a turnover or a missed shot, including four contested shots inside four feet, failed to enhance the 'Eaters' opportunity to top the Bruins for the third time in their eight meetings.
Trailing, 68-63, with 5:18 left, McNealy had a bounce pass stolen to thwart one UCI possession.
Down, 72-67, UCI's Eric Wise missed a driving layup around a defender with 1:09 remaining.
UCLA, which missed eight of 10 free throws in the final 5:26 to avoid sealing the deal, had two misses from the foul line by Jeremi Anderson with 51 seconds left.
On the ensuing possession, Rembert drained a driving layup while being fouled and added the free throw to pull the visitors within two with 39 ticks on the clock.
After a UCLA free throw, Wise, who had a team-high 16 points, missed another shot in the lane and UCLA converted one of two free throws on the ensuing possession.
Senior Darren Moore banked in a three-pointer on which he appeared to be fouled with seven seconds left and the Bruins' two ensuing missed foul shots gave UCI its final chance.
"The places where we tried to go, we went," UCI Coach Russell Turner said of his team's offensive execution down the stretch. "We didn't convert them all, which you're never going to do against a bigger team. But I told my guys I think we've got a chance to be good if we can build on what we've done. We're not good yet, but we've got a chance.