NEW YORK -- Even though they have already secured home-field advantage throughout the American League playoffs, the Rays let the Yankees know in a 4-3 victory on Friday night at Yankee Stadium that it’s not going to be easy for New York to clinch a Wild Card spot against them.

“No matter who you’re playing, you want to try to -- whether you want to call it spoiler or deaden the mood, I don’t even know what word you want to say, but you try to win ballgames,” said Rays center fielder Kevin Kiermaier, who went 2-for-2 with a walk and an RBI single. “And in their situation, they have pressure on them and they know what’s at stake for them. So we want to throw our best at them, and they’re going to do the same with us, so may the best team win. That’s the name of the game.”

Pitching was the name of the game for Tampa Bay. Left-hander Shane McClanahan started for the Rays, tossing three innings and allowing one run on three hits. That run came in the first inning, when Gleyber Torres scored on a single by Giancarlo Stanton.

Rays manager Kevin Cash said they didn’t want McClanahan to go deep into the game. The outing against New York was just a warmup for the American League Division Series, which starts Thursday against the winner of the AL Wild Card Game.

“We felt good about [the outing],” Cash said. “... We didn't want to go too deep in the ballgame with [McClanahan] and felt comfortable that after three innings, he's totally fine and totally full-go for his next start, whenever that is.”

McClanahan turned it over to the bullpen, which dominated for five innings until Andrew Kittredge stumbled in the ninth. Louis Head received the bulk of the work, pitching 2 1/3 innings without allowing a run.

“He’s been doing it all year,” Kiermaier said about Head. “... He’s been great ever since the start, and being optioned 10 or 11 times, whatever it was, and him not ever pouting or hanging his head one time. He’s such an easy guy to root for, and he’s also a guy that you want to see on that mound all the time, because he’s nasty. He has been consistently getting outs for us throughout that whole year.”

Left-hander Josh Fleming took over for Head with one out in the seventh and retired all five hitters he faced. With Adam Conley on the COVID-related IL, the Rays could use Fleming out of the bullpen during the postseason. A starter by trade, Fleming has been throwing harder since he was sent to the bullpen.

Cash was pleased to see Fleming perform in a hostile environment like Yankee Stadium.

“You separate the two because we are asking him to come out of the bullpen and get leverage outs,” Cash said. “It's a little different than following an opener where you're banking innings and you're working a start. He's got to come in ready to go from pitch one and he did.”

The Yankees made it interesting in the ninth inning, scoring two runs off Kittredge to make it a one-run game, but he struck out Rougned Odor to end the game with two runners on base.

The Rays scored enough runs to win their 99th game of the season. Left-hander Nestor Cortes started for New York, and he allowed a first-inning solo homer to Nelson Cruz. It was the 449th career homer for Cruz, pushing him into a tie for 40th on the all-time list with Jeff Bagwell and Vladimir Guerrero Sr.

"I think one of the most memorable homers of my career, just to be by his side," Cruz said of Guerrero. "Definitely the guy that I wanted to be like growing up. To be able to be by his side is definitely a privilege."

The go-ahead run scored an inning later, when Manuel Margot touched home plate on a single by Kiermaier. Wander Franco added a two-run single in the ninth for insurance.

“We needed all of it, [with the way] the score ended. Just a really well-played game, both clubs,” Cash said. “Pitching was outstanding on both sides. Nellie gets us started with the big home run ... and then KK did have a big day ... and then Wander comes up really big for us there in the [ninth] inning to separate it.”