Tampa Bay slipped a game behind Boston at the top of the American League East, falling victim to Baltimore's two power producers and then letting a chance at a ninth-inning comeback get away.
Jones hit his 26th homer of the year in the third to give the Orioles a 3-1 lead and Davis launched his 46th in the fifth for the final run of the game.
Davis leads Detroit's Miguel Cabrera by six in the race for most home runs this season.
Wei-Yin Chen (7-6) allowed two runs on six hits over seven innings to get the win. Darren O'Day came on for his second inning of work in the ninth and promptly gave up a single. Brian Matusz replaced O'Day and issued a walk to put the tying runs on base.
Tommy Hunter was called on to relieve Matusz and retired the next two batters. The game ended when Tampa Bay's Jose Lobaton was thrown out trying to steal third, giving Hunter his fourth save.
Jeremy Hellickson (10-7) took the loss, giving up all four Baltimore runs on seven hits in 4 1/3 innings.