The Rams, who play Orem in the second round, bumped their record to 7-4. Olympus finished 6-5.
"Just very excited," said Austin Peterson, Highland's senior quarterback. "We're glad to have another practice Monday. It was a great game. They are a good opponent. We just came out on top."
Olympus took a 14-3 lead into the fourth quarter, thanks to a pair of touchdowns by Coleman Meier.
His 6-yard run made it 7-3 midway through the first quarter. His 67-yard reception in the second quarter seemed to put the Titans on the brink of victory.
But Highland rallied.
"We just settled down and relaxed," Peterson said. "We just needed to play our game. We came out and fought and never gave up."
Highland nearly scored on the opening possession of the third quarter when the Rams drove from their own 10 to the Olympus 8. But Highland fumbled away the ball on first-and-goal to end a futile seven-minute drive.
Undaunted, the Rams made it 14-6 on Mike Kerr's 29-yard field goal with 9:22 remaining.
After a three-and-out by the defense, Peterson's 21-yard touchdown pass to Jerry Padilla trimmed Olympus' lead to 14-12 with 4:56 left.
"I just saw him open, he beat them over the top and I threw it up there and he made the play," Peterson said. "Our O-line, they did a heck of a job."
Peterson was stuffed on the tying 2-point conversion try, but the Rams' defense held again.
Padilla's 27-yard punt return gave Highland the ball at the Titan 23 with 3:05 left to set up Webber's decisive touchdown.