Following the win, slugger Adrian Gonzalez said that the next two months will all be like playoff games for Boston.
"We put ourselves in that position, so that's basically what we've got," Gonzalez said.
After getting pounded in the opener of this three-game series against their rivals, the Red Sox rallied back to win the last two in their final at-bat -- both game-winning hits coming from the unheralded Ciriaco.
"I hope it's huge," said Red Sox second baseman Dustin Pedroia. "We're not going to get much sleep tonight, which is actually a good thing. We'll get to the field and get ready and get after it. We just have to continue to win ballgames and let momentum and everything build up."
The Red Sox needed the two late-inning thrillers in the Bronx to get back to .500, and reinforce the belief that they can make a run down the stretch.
"They're a talented group, there's no doubt about it," said Yankees manager Joe Girardi.
Saltalamacchia started the winning rally in the 10th by drawing a leadoff walk against David Robertson. Then, there was controversy as Will Middlebrooks, who was squaring around to bunt, got hit on the forearm by the pitch. However, the umpires ruled that it also hit Middlebrooks' bat and it went as a foul ball.
Manager Bobby Valentine was incensed, and was ejected from the game. So, too, was right-hander Josh Beckett, who argued vehemently from the dugout.
Middlebrooks came through anyway, belting a single to left. Ryan Sweeney hit a fielder's-choice grounder to second, putting runners at the corners with one out.
Ciriaco continued his recent torment of the Yankees by hitting a little blooper into right that fell in for the go-ahead hit. With the infield in, Ciriaco's hit landed maybe 10 to 15 feet onto the outfield grass.
"Well, basically, you saw what happened," said Valentine. "We get a guy on base, and then Will guts it out and gets a base hit, and Ryan didn't get a bunt down but advanced the runner. Pedro Ciriaco is there with the nice inside-out base hit. We'll take bloops. We need them."
Ciriaco also had some good fortune on Saturday when his line drive to center knuckled on Curtis Granderson, who stumbled and couldn't make the catch, snapping the tie in the top of the ninth.
Which game-winner did he like better?
"Both were good," Ciriaco said.
Ciriaco's second game-winner made him 11-for-22 against the Yankees this season.
"They were playing in, so when I hit the ball, I thought I had a very good chance," Ciriaco said. "I got a little lucky. Not too hard, not too soft."
Alfredo Aceves, who had blown the save with two outs in the eighth, finished off the Yankees in the 10th to earn the win. The righty gave the Red Sox 2 1/3 big innings.
When it was over, he clutched his fist triumphantly, emphasizing the importance of the victory.
"Last night, we tied the series," Aceves said. "We came from Texas and we tied the series yesterday. We won today. That's what it's all about. Since Spring Training, it's all about the series. We win the series, we have a pretty good chance to win. Emotionally? No emotion. I was just saying, 'Yeah.'"
Lefty Felix Doubront turned in a tremendous performance for the Red Sox. He went 6 1/3 innings, allowing four hits and a run while walking five and striking out eight.
"Felix was great," Valentine said. "For a guy that some people thought shouldn't have been pitching in this big series, he pitched his heart out. I don't know how he could pitch any better."
Doubront was untouched until Russell Martin took him deep with a solo shot to right to open the seventh, slicing Boston's lead to 2-1.
Ichiro Suzuki followed with an infield hit. After Doubront struck out Jayson Nix with his 109th pitch of the night, Valentine summoned righty Matt Albers.
Derek Jeter, who had been just 2-for-18 in his career against Albers, stung a single to right. Ichiro, who had stolen second, was held. On came Andrew Miller and he did a terrific job, getting Curtis Granderson on a medium-depth fly ball to left field that couldn't get the run home, and then Mark Teixeira on a grounder to second.
Miller also retired the first two batters in the eighth, but after giving up a two-out double to Andruw Jones, Valentine called on Aceves for a four-out save.
That hope was gone after just one pitch, as Martin jumped on a first-pitch fastball and stung it up the middle for an RBI single to tie the game.
"It's in the past. The past is the past," Aceves said.
For the third time in this three-game series, the Red Sox broke out first. Adrian Gonzalez started a second-inning rally with a leadoff single to left. With one out, Saltalamacchia drew a walk. Ryan Sweeney broke out of a 2-for-25 funk with a two-run double to center, giving Doubront a 2-0 lead.
Despite five walks over the first six innings, Doubront took a two-hit shutout into the seventh.
"That was fun," Doubront said. "I was just looking to pitch. I wasn't scared to pitch here. I just wanted to get the job done, and that's what I did."
The same could be said for the Red Sox, though it was anything but easy.
"We're trying to win series now," said Valentine. "That's the name of the game, and two out of three is a series. We did it the hard way after losing the first and battling two tough games. I'm proud of the guys. That's a great effort."