It was the second tough road game in two nights for Davis (1-1), which fell at Alta to open the season Tuesday.
"I thought when I scheduled this back-to-back that I had to be crazy to do it," Davis coach Jay Welk said. "I have a ton of respect for this program, this coach [Jeff Gardner], and the same for Alta. We'll take so much from this game tonight."
Davis went up 45-44 when Jesse Wade hit a pair of free throws with 5:18 left in the game.
The margin went up to four when Wade found teammate Elijah Kletzli under the bucket, got him the ball for a bucket and eventually an old-fashioned three-point play when Kletzli was fouled then hit the free throw.
"Jesse Wade was our leading scorer last year as a sophomore. He's a guy who can score," Welk said. "We have a ton of confidence in him with that shot [a 10-foot jumper]. He took what was a good shot and traded it for a better shot. That says a lot about him."
Kletzli, a 6-foot-6 senior, finished with 14 points to lead the Darts, while Wade added 11. But it was the free-throw shooting of senior Abel Porter, who had 12 points and 10 rebounds, that saved Davis and an otherwise spotty performance from the charity stripe in the last two minutes.
Osa Masina got off a shot with 17 seconds left in the game and his Bengals (1-1) down 51-49. But Masina, who had a game-high 22 points, missed and Porter then swished a pair of free throws to stave off the Bengals' last try.
Brighton also got 10 points from Chandler Gee, but the home team was without the services of 6-4 junior scorer Brock Miller.
"They're missing a really, really good player, and when they get him back they'll have so many weapons," Welk said.