ST. PETERSBURG, Fla. -- The Tampa Bay Rays entered Tuesday's game with a 1-6 head-to-head record against the New York Yankees and seemed to be on the verge of adding to their dismal mark after falling behind 2-0 in the first inning.

Two runs in the seventh followed by two more in the eighth changed things, though, as the Rays earned a 4-2 comeback victory to move back to three games behind the American League East-leading Yankees.

"The way the game started, I don't know if we saw it coming that way, that ending like that," Rays manager Kevin Cash said.

Facing a two-run deficit against Yankees starter Nathan Eovaldi, the Rays finally got to the right-hander in the seventh when designated hitter David DeJesus continued his recent tear by lining a two-run single to center.

The Rays took the lead in the eighth.

Center fielder Kevin Kiermaier walked with one out and advanced to third on a single to right by right fielder Steven Souza Jr.

After Yankees reliever Dellin Betances replaced Eovaldi (3-1), Kiermaier scored on a sacrifice fly to center by third baseman Evan Longoria.

With Rays second baseman Logan Forsythe batting, Betances threw a wild pitch that plated Souza.

"I felt like I tried to do too much with Kiermaier up there and I just let him go on four straight," said Eovaldi, who walked two over his 101-pitch outing. "That's the most frustrating thing about it. I was just trying to make those perfect pitches instead of just challenging him and make him put the ball in play."

Rays starter Chris Archer loaded the bases to start the game by giving up singles to center fielder Jacoby Ellsbury and left fielder Brett Gardner and a walk to designated hitter Alex Rodriguez. Yankees catcher Brian McCann and right fielder Carlos Beltran followed with run-scoring singles.

New York seemed on the verge of a bigger inning, but Archer struck out third baseman Chase Headley, induced second baseman Stephen Drew into a flyout to center and forced first baseman Garrett Jones into a groundout to second.

"It would have been nice to get more at the start," said Ellsbury, who finished 2-for-4 to raise his season average to .346. "That's the time to strike, but that's what good pitchers do. He pitched well after that."

After escaping damage in the second inning following consecutive one-out singles, Archer went the rest of his seven-inning outing by giving up just one hit. Archer threw 105 pitches, and he surrendered two runs on seven hits and one walk while striking out eight in a no-decision.

"I was honestly not thinking about the situation," he said of his early difficulties. "I was just thinking about executing my pitches, and I knew that the hits that they were getting, that wasn't going to beat me if I stayed down in the zone, use my fastball, use my slider. I just stayed in the present moment and was able to work through the first."

Rays right-handed reliever Kevin Jepsen (1-2) pitched a hitless eighth, and closer Brad Boxberger recorded his ninth save with a scoreless ninth.

Eovaldi was in the zone until the seventh inning. After giving up an infield single to Souza with one out in the first, the right-hander stuck out Longoria and picked off Souza to end the inning.

Eovaldi then retired the next 10 batters before allowing another infield single to Forsythe and a broken-bat single to center by DeJesus with one out in the fifth. Eovaldi got out of the inning, though, by forcing shortstop Asdrubal Cabrera into a fielder's choice out before striking out left fielder Brandon Guyer.

The Yankees starter wound up allowing four runs on six hits and two walks with six strikeouts in 7 1/3 innings.

NOTES: Yankees RHP Ivan Nova (Tommy John surgery in April 2014) threw 33 pitches over three innings in an extended spring training game Tuesday in Tampa, Fla. He is scheduled to pitch again Monday. ... Yankees RHP Masahiro Tanaka threw a 30-pitch bullpen session, his first since landing on the disabled list in late April due to a strained right forearm and tendinitis in his right wrist. His next step will be determined after Wednesday. ... Manager Joe Girardi and a plethora of Yankees players sent Yogi Berra a happy birthday greeting via FaceTime on Tuesday. ... Following Tuesday's game, Rays manager Kevin Cash decided on having RHP Erasmo Ramirez start Thursday's contest. ... Rays 3B Evan Longoria likely will hit third in the batting order moving forward, according to Cash. Longoria is batting .214 (3-for-14) in the third hole and .293 (29-for-99) batting fourth this season.