Baltimore (45-30) now heads out on a nine-game West Coast road trip on a five-game winning streak. Tampa Bay (31-43), meanwhile, has dropped 11 straight.
Power carried the Orioles yet again, as Davis' homer in the first gave them a quick 4-0 lead. Schoop's solo homer and Trumbo's two-run blast gave the Orioles some insurance as the Rays battled back to come within a run at one point.
Baltimore, however, scored the game's final six runs.
"This was a fun series," said Baltimore's Adam Jones, who went 4-for-4 in the win.
"Obviously, we did a lot, scoring a lot of runs each night. But we just passed the baton."
The Orioles finished with 31 runs in four games and banged out nine homers -- despite going without one in the opener of Saturday's doubleheader.
Tampa Bay is reeling from numerous injuries, and the Orioles jumped on the Rays, scoring two come-from-behind victories and continually crushing the ball.
"We caught them when they've got a lot of people hurt and you're hoping to take advantage of it before they get out of town because the next time we seem them, trust me, they'll be a different club," Orioles manager Buck Showalter said.
Trumbo had three RBIs overall, and Jones led a 17-hit Baltimore attack with his big day. Schoop extended his hitting streak to nine games with three hits, and Manny Machado also added three hits.
Desmond Jennings and Oswaldo Arcia both hit solo homers for Tampa Bay, which touched up Orioles starter Tyler Wilson for five runs on 10 hits in just five innings. Still, Wilson (4-5) came away with the victory.
Rookie Dylan Bundy gave the Orioles another strong effort out of the bullpen. He took over in the sixth and threw three shutout innings, which gave the bullpen some needed rest and impressed the skipper.
Rays starter Drew Smyly entered the game with a 4-0 career mark versus Baltimore, but his past performance was meaningless in this game as the Orioles scored six times in the first three innings.
Smyly lasted five innings but surrendered eight runs on 10 hits and fell to 2-8, now losing four straight.
"They're hitting good pitches," Smyly said. "It just seemed like every ball found a hole. It's no denying they kind of beat me up today."
The Rays did not help by missing several quality scoring chances. They finished 1-for-8 with runners in scoring position and stranded eight.
The Orioles started quickly as Jones walked to open the bottom of the first while Joey Rickard and Machado both singled to load the bases. Davis then sliced a shot into the left-field seats for his seventh career slam on a 1-2 pitch.
"(Smyly) threw a fastball out over the plate, and I got enough of it to hit it out," Davis said. "I was glad to come back and have a productive at-bat after two not-very-aggressive swings."
Jennings homered to start the second for Tampa Bay, but the Orioles answered in the bottom half. Nolan Reimold doubled and went to third on Francisco Pena's sacrifice bunt.
Jones then dropped a perfect bunt up the first-base line. He beat it out for an infield single, and Reimold scored from third on the squeeze as the Orioles took a 5-1 lead.
Schoop made it 6-1 with his solo shot to left in the third inning. Arcia followed suit in the fourth, his first homer with Tampa Bay, which acquired him Friday from Minnesota.
The Rays added three more in the fifth. Logan Morrison lined a two-out RBI double to left, and Arcia smashed a two-run double to right that cut the lead to 6-5.
Arcia went to third on the throw but Wilson got Tim Beckham on a grounder to keep the lead.
Trumbo then belted a two-run homer for an 8-5 lead in the bottom of the fifth. The Orioles then broke the game open with four runs in the eighth.
"Losing is tough," Rays manager Kevin Cash said.
"Nobody's character is going away. We're staying positive."
NOTES: Baltimore LHP Ashur Tolliver was optioned to Triple-A Norfolk after the game. He earned his first major league win in Friday's victory and will be going on paternity leave in the coming days. ... Orioles manager Buck Showalter said RHP Darren O'Day (right hamstring strain) threw well Saturday. Showalter said that if everything went right, O'Day could be activated during the West Coast trip. ... Rays RHP Tyler Sturdevant was sent back to Triple-A Durham to make room for RHP Ryan Webb, out since May 27 with a right pectoral strain. ... Baltimore also sent Danny Farquhar back to Durham after he was the team's 26th man in Saturday's doubleheader. Both Farquhar and Sturdevant pitched in the twinbill, which Baltimore swept.