There were a couple of key plays that went UCLA's way. At the end of the half, as their receiver went out of bounds with less than 1 second left, the timekeeper stopped the clock before the ref asked for the stoppage. Now perhaps replay would have placeed 1 second back on the clock, ala Texas-Nebraska, if it hadn't been prematurely stopped, but they might not have.
The subsequent FG made it 21-10 at the half, and gave UCLA a little momentum, which they've never lost. Of course, they might have lost that momemtum if Temple had properly been given a 1st and goal at the 8 yard-line when they were still ahead 21-17 in the 3rd quarter. The ref made a mistake of marking it about a foot short, but the replay should have fixed that, as he was clearly over the yellow line with the ball when his elbow hit.
UCLA was fortunate to get out of cold DC with a win.