ST. PETERSBURG -- After five innings Saturday afternoon, the Rays had managed to collect one hit and one walk against Yankees ace Gerrit Cole. They’d been held scoreless in 22 of this series’ first 23 innings and limited to only two runs over their previous 30 innings. If they were going to break out of that slump, especially against Cole, they needed something to go their way.

• Box score

Fortunately for the Rays, they caught a few late breaks and pulled out a 3-1 win before a sold-out crowd of 25,025 at Tropicana Field. With starter Corey Kluber and Tampa Bay’s bullpen cruising, the lineup found enough hits to push past Cole and secure the club’s seventh comeback win of the season.

The Rays didn’t exactly bash the ball around the ballpark, recording only two extra-base hits and two hits that qualified as “hard-hit,” according to Statcast. Instead, they beat the Yankees for the first time this season with a couple of timely walks, a 64.5 mph game-tying single, a key bloop double that came off Francisco Mejía’s bat at 74.9 mph, some seventh-inning small ball and a whole lot of pitching.

“Sometimes you hit the ball really hard and you don't get anything out of it, so today, we didn't hit the ball hard and we were able to score some runs,” third baseman Yandy Díaz, whose seventh-inning infield single put the Rays ahead, said through interpreter Manny Navarro. “However we've got to do it, we'll do it.”

After a leadoff walk to Díaz, Cole retired 14 consecutive batters and carried a no-hitter into the fifth. But Kluber, facing his former team, kept the Rays in the game with an excellent start of his own. As manager Kevin Cash put it, “He had to be good because of the guy that we're facing on the other side.”

Kluber’s outing didn’t start well, as the Yankees had a 1-0 lead three batters into the game, but he settled in and allowed just one hit the rest of the way. He struck out five without a walk and retired the last 10 batters he faced during his efficient six-inning outing.

“When you're going up against a guy that's throwing the ball really well, [you’re] just trying to keep it as close as you can and give the offense an opportunity to come through,” Kluber said.

Eventually, the Rays did just that.

With two outs in the sixth, Cole got ahead of Ji-Man Choi by throwing his first two pitches for strikes. But Choi, a longtime nemesis of Cole, took three pitches and fouled one off to work the count full. Cole fired an up-and-away fastball that he thought was strike three, but home-plate umpire Edwin Moscoso called it ball four, keeping the inning alive.

Wander Franco took four straight pitches to walk, bringing up Randy Arozarena for the Rays’ first scoring opportunity of the game. Arozarena slapped a cutter -- Cole called it a “great pitch” -- to left field for a soft game-tying single.

“As long as it lands where there is nobody,” Arozarena said through Navarro, “I'm always going to be happy.”

Cole exited after six innings, leaving the game to be decided by both bullpens, and the Rays struck first in the seventh. Kevin Kiermaier smacked a leadoff single to center field against lefty Lucas Luetge, then hustled to third when Mejía’s bloop to right field landed just inside the line for a double.

“There weren’t a ton of hard-hit balls,” Cash said. “But given the stretch that we've been on, obviously, you'll take it.”

The Rays’ first attempt to get a runner in from third failed, as Kiermaier was cut down by first baseman Anthony Rizzo on a grounder hit by pinch-hitter Harold Ramírez. The Yankees turned to right-hander Michael King, who coaxed a potential double-play grounder from Taylor Walls that moved up Mejía to third when Walls hustled to beat the throw to first.

“I think we've come to expect and appreciate, more than anything, the way they go about their business,” Cash said. “You can be frustrated, but there are little things that you can do to keep the inning going -- and he definitely did that.”

Up came Díaz, who bounced a two-out single to the left side of the infield and reached safely without a throw from third baseman DJ LeMahieu, bringing home Mejía and giving the Rays a 2-1 lead.

While Rays relievers J.P. Feyereisen, Jason Adam and Colin Poche put up zeros, the Rays padded their lead in the eighth. Franco ripped a leadoff triple down the right-field line and scored on a single by Manuel Margot, who extended his hitting streak to 15 games and gave the bullpen some breathing room.

“Like we say: If you can't hit the starter, you hit the reliever,” Margot said through Navarro. “So that was our plan.”

The past few days, the Rays have been searching for something to get their lineup going. Unconventional as it may have been, could this game have done it?

“I think the doors opened for all the hits,” a smiling Díaz said through Navarro. “So from here on out, I think all the hits are coming.”