ST. PETERSBURG, Fla. — The kind of inning that only existed in the Yankees’ hopes and dreams over the last three weeks finally happened in the flesh Thursday afternoon.

That it came against one of the best pitchers in baseball who had shut them out in two starts earlier this season, well, “That’s baseball, Suzyn,” Aaron Boone said from his office as music blared in the winning clubhouse next door.

Whatever the Yankees offered up as a sacrifice during their hitters meeting Thursday morning, it worked, as their bats finally broke out of an extended slumber for a six-run third against Drew Rasmussen that fueled a 12-4 win over the Rays to salvage a series split at Tropicana Field.

The six runs the Yankees (51-42) scored in the third inning were more than they had scored in any full game since June 17, after which they began what was a 5-15 tailspin entering Thursday. But at least for a day they made good use of their bats to finish the four-game set on a high note and get back within four games of the Rays (54-37) for first place in the AL East.

“We needed a good one like that,” said Ryan McMahon, who delivered a pair of RBI doubles, including one on the game-changing at-bat with a 12-pitch battle in the third inning. “We needed a good one like that where we stacked good at-bats, had good energy against a really good baseball team. That team over there, they’re definitely a tough squad. To do it against them definitely feels good.”

On a day that began with Brian Cashman acknowledging that “the storm is upon us right now,” and giving votes of confidence to both Boone and hitting coach James Rowson, the Yankees snapped out of their offensive malaise with 14 hits while piecing together a bullpen game, as seven relievers did enough to get by.

Ben Rice clubbed a pair of home runs — giving him six in his last nine games and 28 on the year — and drove in five runs while Austin Wells added his first homer since May 22, finally showing signs of life in the midst of a brutal offensive season.

“The great thing about it was, it was everyone,” Boone said. “When they would answer, I feel like we had an answer to come back, too, to add on and protect the lead. Really good day for us, obviously with what we’ve been through, and hopefully one that gets some guys settled and we can continue it on this weekend.”

Max Schuemann, who went 2-for-4 and delivered a spark with a double that led off the decisive third inning, credited Jazz Chisholm Jr. for speaking up during the pregame hitters meeting and providing some energy that set the tone for the day.

“[The message was] just that we’re obviously better than how we’ve been playing,” Schuemann said. “Stacking good at-bats together and not folding. … Feel like it really brought the guys together. I think it needed to be said.”

Rasmussen, the Rays All-Star who had thrown 13 shutout innings against the Yankees this season before Thursday, retired the first six batters on 26 pitches before Schuemann led off the third inning with a double.

McMahon then entered a battle with Rasmussen, including fouling off seven pitches on the way to a full count before roping a double down the right field line to tie the game at 1-1.

“As you’re fouling more pitches off, you’re gaining more and more confidence,” McMahon said.

Wells followed by flying out to move McMahon to third, but the next five Yankees all reached on hits to knock Rasmussen out of the game in improbable fashion. Trent Grisham doubled, Rice clubbed a two-run shot, Jasson Domínguez and the badly slumping Cody Bellinger hit back-to-back infield singles and José Caballero added a single through the open right side on a hit-and-run for the 5-1 lead.

After Rasmussen hit the showers, Chisholm — the only starter without a hit, but who delivered some strong defense at second base — capped off the inning with a sacrifice fly to make it 6-1.

Of course, given how things have gone for the Yankees lately, it did not all come easy from there. But unlike most games over the past three weeks, any time the Rays answered, the Yankees did, too, to put together a feel-good win.

“It definitely boosts our morale heading into the next series,” Rice said. “We just got to keep that momentum going, keep that energy going and hopefully we can continue what we need to do.”