Boston will try and carry that momentum into Sunday's finale and go for a series split before heading into the All-Star break.
Playing from behind during a majority of the series, the Red Sox's pitching staff has combined to surrender 12 runs in the first inning, including three home runs.
"We just have to keep them from scoring in the first inning and give the offense a chance, a feeling that they can play their game," Red Sox manager Bobby Valentine said. "Catching up is tough."
Red Sox left-hander Jon Lester, coming off a solid start against the A's, will try and break that first-inning streak.
Lester took a no-decision on Tuesday against Oakland, allowing just one run on four hits over 6 2/3 innings. He also struck out a season-high-tying nine batters.
Meanwhile, Ivan Nova will be on the hill for the Yankees, looking for his first win since June 17.
The right-hander took the loss in his previous outing against the Rays, giving up six runs (three earned) on seven hits. Struggling with his fastball command throughout the game, Nova lost for the first time since May 19.
However, Nova and the rest of the Yankees feel confident that they can get the win on Sunday and go into the All-Star break with a series win against their American League East rival.
"We're just trying to do our thing, stay consistent in what we're doing," Yankees outfielder Nick Swisher said. "As you can see, it's just nice and relaxed in here, man. It's nice. It's nice to be in that spot. We feel like we've had a great first half, we've got one more to go, and then we can enjoy that All-Star break."
Yankees: Martin breaks hitless streak
After going 30 at-bats without a hit, Russell Martin broke out of his dry spell in Saturday's night game against the Red Sox, belting a double down the left-field line in the second inning.
Before the double, Martin hadn't recorded a hit since June 20 vs. Atlanta, dropping his batting average to .176.
"You worry a little bit [about Martin]," Yankees manager Joe Girardi said before Saturday's nightcap. "Every hitter's been through it, almost. I've got to believe if you've played a substantial amount, everyone's been through an 0-for-20 or a 1-for-30. It's part of the game, but it doesn't make it any easier when you're going through it."
Red Sox: Sweeney activated from DL, Kalish optioned
Prior to Saturday night's game against the Yankees, the Red Sox activated Ryan Sweeney from the 15-day disabled list and optioned Ryan Kalish to Triple-A Pawtucket.
Out since June 17 with left big toe inflammation, Sweeney started in center field and hit seventh on Saturday. He finished the night going 1-for-5.
"Just one of those things where you need a little time off," said Sweeney Saturday morning.
The Yankees are 49-19 this year when hitting at least one home run and are 35-8 when hitting multiple home runs.
Nova is 1-2 with a 5.70 ERA in five career appearances against the Red Sox, having allowed four earned runs in three of those outings.
Red Sox first baseman Adrian Gonzalez is hitting .377 (29-for-77) with nine RBIs and 11 runs scored during his season-high 18-game hit streak.