Tampa Bay did so on Monday with a 4-3 win over the Yankees and will try on Tuesday to make it back-to-back victories to secure a series win. Monday's decision trimmed New York's lead over Tampa Bay to 6 1/2 games.
"You've just got to do your part as a player on this team," said James Shields, who will start for the Rays on Tuesday night at Tropicana Field. "When everybody does their part, I think it goes hand in hand with wins. Obviously, it's one step at a time. We're not panicking or anything like that, but we know we definitely have to get better all around.
"We definitely want to win the series, there's no doubt about it. That's what we've tried to do all season long, is try to win the series. It's not going to be any different than any other time."
Shields will look to shake off struggles he encountered in his last start, against Detroit, and help Tampa Bay move up in the AL East standings.
The right-hander surrendered four runs and a career-high 14 hits over 7 2/3 innings on Thursday for his fifth loss of the season. He did strike out six and walk only one, however.
Meanwhile, Ivan Nova will take the mound for the Yankees, hoping to have his June success carry over to July.
In June, Nova went 3-0 with an ERA of 1.59, tossing four quality starts.
Nova is also thriving on the road; he's undefeated in his last 16 starts away from Yankee Stadium, a streak that dates back to June 20, 2011. The right-hander has gone 12-0 with a 3.17 ERA over that stretch, which, according to Elias Sports Bureau, is the fourth-longest such streak in Yankees history.
Nova held the White Sox to one run on six hits over 7 1/3 innings in his last start but took a no-decision after the bullpen couldn't hold a lead. David Robertson surrendered a lead-changing three-run home run in the top of the ninth inning to set up the Yankees' first loss with Nova on the hill since May 19.
"It's tough; it stinks," Robertson said afterward. "We had the game right there. A couple things didn't go our way. I made one bad pitch, and they made me pay for it."
Yankees: Cano named AL Player of the Week
Second baseman Robinson Cano was named AL Player of the Week on Monday. Cano hit .414 (12-for-29) with four home runs and 10 RBIs in seven games last week, during which the Yankees went 5-2.
In New York's three-game sweep of Cleveland, Cano batted .500 (6-for-12) with two homers and five RBIs. For the season, he is hitting .313 with 20 homers, 23 doubles and 47 RBIs.
"I think it's pretty close to what Robbie is," Yankees manager Joe Girardi said. "Maybe he's not a .340 hitter every month. And what'd he hit, 11 home runs? Maybe not that. But for Robbie to hit .330 during the course of a season would not shock me. I think it's who he is, for the most part."
To clear room on the 25-man roster for recently acquired reliever Chad Qualls, the Yankees optioned struggling right-hander Cory Wade to Triple-A Scranton/Wilkes-Barre on Monday. Qualls pitched two-thirds of an inning in Monday's game, recording one strikeout.
Rays: Hellickson likely to make next start
Right-hander Jeremy Hellickson expects to make his next scheduled start -- on Thursday at Cleveland -- after throwing a 40-pitch bullpen session on Monday. Hellickson sustained a bruised right shin and was forced to leave Saturday's 6-2 loss to the Tigers after being struck by a third-inning line drive just below the knee.
"It's still a little sore, I guess, but it's tolerable, and I threw my bullpen [session] just fine," Hellickson said. "It didn't really affect it at all; it just felt normal."
The Yankees have lost just one of their last nine series, going 7-1-1 over the stretch.
The Yankees have hit a Major League-high 124 home runs this season, including 23 over their last 12 games.
The Rays have used a starting pitcher 30 years old or younger in 975 straight games, a Major League record.