With 31 seconds remaining, Thompson found running back Danzel Williams on an 8-yard swing pass for the touchdown.
Thompson finished 7-for-9 for 42 yards and the touchdown, while he also rushed for 25 yards on three carries.
But it was wide receiver Trey Metoyer, the new kid on the block, who really stole the show.
He racked up a team-high 72 receiving yards on six catches and demonstrated that athleticism everyone's been talking about.
Blake Bell proved to be the quarterback that really highlighted the entirety of the day, completing 14-of-19 for 179 yards and a deep touchdown.
"Offensively, I thought of course Trey showed what I have been talking about all spring with his abilities to make plays," said OU head coach Bob Stoops. "I thought the offense did a great job, just overall taking care of the football. It wasn't sloppy. We had two Big 12 crews officiating it and didn't have a lot of line-of-scrimmage penalties.
"So it was pretty clean for your spring game when there are so many guys playing. Some guys are not ready to play yet and played well overall."
One of those that is ready and did play well was wide receiver Jaz Reynolds, who finished with a couple of catches and 64 yards.
He was the beneficiary of that long toss in the first half, as he raced downfield, hauled it in and dunked the ball over the cross bar.
Quarterback Drew Allen, another backup, finished 10-of-18 for 72 yards, while starter Landry Jones led the team downfield on the first drive, going 4-for-8 for 23 yards in guiding the White Team to an opening field goal.
"The first drive took quite a bit of time off the clock, so we went half of a quarter," said OU offensive coordinator Josh Heupel. "The first drive ended in a positive way. I would've obviously liked to get seven instead of three. I felt like it was a positive first drive, took him out and gave those guys a bunch of work."
Defensively, though, there were some solid performers as well.
After they trailed by double digits early in the new Red-White scoring format, they really settled in and showed more discipline.
"When we play together, we're really solid across the board," said OU defensive coordinator Mike Stoops. "I think we're going to be a very complete defense."
McFarland, Phillips and Peterson finished with three of the Red Team's 14 tackles for loss.
Defensive back Julian Wilson led the team with two tackles for loss, including a seven-yard sack, part of his team-leading eight total tackles.
Linebacker Corey Nelson also racked up eight tackles, while the secondary shored up and only allowed the one deep ball on the day.
Cornerback Demontre Hurst anchored that group and finished with five tackles, as well as a pass broken up.
The defense also produced without several guys on the defensive line, including defensive end R.J. Washington and tackles Stacy McGee and Casey Walker.
"When we come back in August, we'll have some guys that weren't with us today that we desperately need," Mike said. "Our pass rush needs to improve, but we'll need to continue keeping position on the football when it comes to deep balls."
It was an evenly competitive game and one that really stayed close throughout, as the defense owned a 21-15 lead late before the offense stormed back late.
One other player who had a solid day was running back Brennan Clay.
He led the backs with 65 rushing yards on 10 carries.
This event concludes spring ball for OU, who will open up fall camp, as Mike alluded to, in early August before facing UTEP in the opener Sept. 1 in El Paso, Texas.