ST. PETERSBURG — Tampa Bay’s relentless contact-oriented lineup chased American League Cy Young Award favorite Cam Schlittler from the game during a four-run fifth inning Monday night at Tropicana Field, giving the Rays a 2-0 lead in the American League Division Series and putting them one win from the AL Championship Series.

The victory puts history firmly on Tampa Bay’s side. Teams with a 2-0 lead in best-of-five postseason series have gone on to win 83 of 93 times, an 89% rate. Teams that have won the first two games at home in Division Series play under the current 2-2-1 format have advanced 33 of 36 times, a 92% clip.

“It’s pretty significant,” manager Kevin Cash said. “It’s going to be challenging, but we’ve set ourselves up in a good way by getting on a plane here up 2-0.”

The Rays drew first blood in the opening inning, capitalizing on a three-error frame from the Yankees. Yandy Díaz reached on an error by third baseman Ryan McMahon, advanced to second on a single by Jonathan Aranda, then scored when New York threw away a potential double-play grounder by Junior Caminero. Yankees catcher Austin Wells acknowledged what Tampa Bay’s approach does to opposing defenses. “Put the ball in play, and good things happen,” Wells said. “For them, it happens a lot.”

That contact pressure proved too much for Schlittler in the fifth. Aranda led off with a single, and Caminero crushed a 112.4 mph double to right-center to put two runners in scoring position. Liam Hicks drove in Aranda with a groundout, then Chandler Simpson — the hardest Rays hitter to strike out — slapped a grounder to the left of the mound that shortstop George Lombard Jr. couldn’t handle, extending the lead to two runs. Simpson stole second, and Lombard committed another error on a ball hit by Jonny DeLuca, setting the table for Richie Palacios, who ripped a two-run single up the middle on the eighth pitch from lefty Brent Headrick to cap the rally.

Schlittler finished with just two strikeouts — the fewest of his young career and tied for the fewest in any game he has pitched — after failing to record a strikeout in the first two innings for only the third time in his career. “They put pressure on you, and they find ways to get those runs across,” Schlittler said.

Tampa Bay struck out less than any other team in the majors this season, a fact that showed up all night against the Yankees’ ace. Palacios, who finished second on the team with 31 two-out RBIs during the regular season, delivered the knockout blow. “He seems, as much as anybody in our lineup, to really rise to the occasion when we need him to come through,” Cash said. “He’s come through so many times for us.”

Closer Bryan Baker recorded the final three outs after lefty Ian Seymour handled the previous six. “That’s Rays baseball right there,” Baker said. Shortstop Taylor Walls, asked before the game how Tampa Bay planned to approach Schlittler, kept it simple: “Just kind of do what we’ve been doing all year.”

“Constant pressure, constant long at-bats, getting pitches to hit. It’s our M.O. all season long,” Cash said. “We’re a contact-oriented team with guys that can knock the ball out of the ballpark, as well.”

The series shifts to Yankee Stadium for Game 3, where the Rays will have three chances to close out the series and advance to the AL Championship Series.