The Orioles won their fourth in a row, the last two wins coming over Pittsburgh after the Pirates had captured six out of seven.
Emergency starter Jake Arrieta (3-8) struck out nine over seven innings to get the win, which was made easier by a 13-hit Baltimore attack.
Davis doubled home the Orioles' initial run in the first inning and added a two-run blast in the seventh. Betemit had an RBI double in the second, a sacrifice fly in the fourth and a solo homer in the sixth.
Arrieta was called on to start in place of Brian Matusz, who was hit on the nose by a ball while fielding bunts during practice. Arrieta had recently been removed from the rotation after losing six straight decisions.
He gave up the only Pittsburgh run on seven hits.
Kevin Correia (2-6) took the loss, giving up four earned runs on 10 hits in six innings.