Davis' Mitch Parkinson tied the game in the 54th minute, but it was Coffey's speed that led to the winning goal.
Coffey sprinted along the far side and beat his defender. He crossed it to Perkins, who nailed it.
"I knew he would serve it up on a plate," Perkins said. "I wasn't surprised at all."
For two teams that hadn't given up a goal all season, it was a high-scoring affair. Brighton started it off in the 14th minute with Andrew Campbell finishing a Connor Forham free kick from midfield. Parkinson answered in the 29th minute to enter halftime deadlocked at 1-1.
"It was a slugfest like we thought it would be against Davis," Brighton coach Russ Boyer said. "[Davis is a] great team, very well-coached. We expected a battle."
Parkinson, who scored the game-winner in last year's state title game, finished the day with two goals.
Brighton's success came from spreading the field and being patient on the attack. Led by Campbell and Seth Fankhouser's midfield ball handling, the Bengals were able to develop plays and finish. With two goals coming from free kicks, Boyer was impressed with his team's execution.
"We did a really good job on our offensive dead balls," Boyer said. "We're very dangerous on playing those balls in."
Boyer expects games like Tuesday's to pay off when the Bengals open region play Friday.
"It's nice to get a tough game under our belt," he said.
Storylines Brighton 4, Davis 3
R Brighton earns a bit of revenge in a rematch of last year's Class 5A state championship game. Davis won the state title game 1-0 last May.