Baltimore, losers in six of eight games at home, remained in third place and dropped out of the second AL Wild Card spot with Detroit's win over Minnesota.
"I think you've got to be realistic about where we are at this point after losing four," Orioles closer Zach Britton said. "It's kind of time to light a fire under our [rear ends], because those other teams playing for the Wild Card are right there. You kind of need to look over your shoulder if you want to live in reality. You can't just assume if we lose another game here and there it's OK. We need to find a way to win games. It's plain and simple."
Boston chased Baltimore's Opening Day starter, Chris Tillman, from the game after five outs -- the ace's shortest start of the year -- jumping out to an early three-run lead. Price, who allowed all three of his runs on rookie Trey Mancini's homer, held firm from there, as Boston went back up on Andrew Benintendi's RBI single in the fifth, while Hanley Ramirez went deep in the seventh inning.
Ramirez's insurance run, which snapped O's reliever Donnie Hart's 18-inning scoreless streak, helped the Sox secure their first back-to-back four-game sweeps since July 1-7, 1968, vs. Oakland and Minnesota.
"We're playing baseball the way we're supposed to be playing it," said Red Sox designated hitter David Ortiz, who played his final regular-season game at Camden Yards. "This time of year, every game matters. We're taking it personally."
"It was alright," Ortiz said of the gag gift. "You know, I just thank Baltimore for the memories and see you in the playoffs."
MOMENTS THAT MATTERED Hanley heats back up: Fresh off winning the AL Player of the Week Award, Ramirez had been quiet in this series until the finale. The first baseman gave the Red Sox the lead with an RBI single in the first, and his opposite-field homer to right gave Price a 5-3 lead in the seventh. It was Ramirez who started this eight-game winning streak for the Red Sox by clocking a walk-off, three-run homer on Sept. 15 against the Yankees.
"I'm not hot yet," claimed Ramirez. "It's coming. It's coming. I'm just going out there and trying the best I can on the field."
Tillman's abrupt exit: The O's ace couldn't come up with the big start his team so badly needed, instead going just 1 2/3 innings and putting the Orioles in an early hole. Tillman's outing marked the seventh time this season Baltimore has gotten a starting pitching performance shorter than two innings, with both Boston and Toronto combining for just one. The O's pitched to a 6.38 ERA over the four-game set.
"I was just mechanically bad tonight," Tillman said. "The more I tried to make an adjustment, the worse it kind of got for me. I just couldn't hit on a consistent basis. I'd hit one and then miss three. It wasn't good. Command was bad from the get-go. I was never able to find it." More >
Mancini to the rescue: The O's rookie, who homered for his career first hit on Tuesday, again came up big for the big league club. Mancini, who also doubled, put Baltimore on the board against Price and now has four RBIs in his first two career starts.
"At the moment, it's just an unbelievable experience, and I had a lot more of my family here today, so it was great that they got to see that," Mancini said. "But on the flip side, after a loss like that, it kind of, you don't really think about the home run so much. It really doesn't matter."
Price dials it up after losing lead: Annoyed by losing the lead on Mancini's three-run shot, Price locked it in for the rest of his outing, retiring 13 of the final 15 batters he faced. Mancini's double was the only hit Price allowed in his final 4 1/3 innings.
"I threw an elevated changeup in the middle of the plate to a guy that just came up and he's swinging the bat well," said Price. "Other than that I think I made pitches when I needed to, with the exception of the third inning. But that was a big win." More >
QUOTABLE "When you are down, they are going to step on you, and when you're up, you are going to ride the flow as much as you can. It's all about riding the good times and shortening up the bad times as much as you can, and we are going to try to shorten this one up starting tomorrow." -- Orioles manager Buck Showalter
SOUND SMART WITH YOUR FRIENDS Hart, who allowed his first career Major League run to Jackie Bradley Jr., owns the second-longest scoreless streak (in games) for an Oriole to start a season at 18 games. He trails only Will Ohman, who started the year with 25 scoreless outings April 6-May 25, 2010.
In September, the Red Sox lead the American League with a 2.80 ERA. In all of baseball, only the Dodgers have a better ERA this month.
WHAT'S NEXT Red Sox: The Red Sox head to Tropicana Field to play the Rays for the middle portion of this three-city, 10-game road trip. First pitch is scheduled for 7:10 p.m. ET on Friday night. Lefty Drew Pomeranz, who struggled mightily with abbreviated outings his last two times out, will try to rebound. The Rays counter with right-hander Chris Archer.
Orioles: Baltimore will send Yovani Gallardo to the mound for the series opener against Arizona on Friday at 7:05 p.m. ET. The righty allowed six runs on seven hits over 3 1/3 innings on Thursday against the Rays, and he will try to rebound against the D-backs.