Matt Joyce had a two-run single in the first inning for Tampa Bay, which moved within two games of Boston for the lead in the wild card standings. The Rays lost three of four games in the Bronx, but will now head home to finish the season with three this weekend against Toronto and then a trio vs. the Yankees.
"You've got to run the table, but you have to do it on a nightly basis," Rays manager Joe Maddon said. "As you're trying to do that, if you hit a bump in the road you still have to stick with the math. The math still works. You cannot give up."
The Red Sox, who were idle Thursday, play on the road against the Yankees this weekend before ending the season in Baltimore.
The Angels entered the day tied with Tampa Bay in the wild card standings, but lost in 12 innings to Toronto thanks to Edwin Encarnacion's home run.
Matt Moore (1-0), in his first major league start and third career appearance, had 11 strikeouts through five innings while giving up just four hits.
"Fortunately we put up a lot of runs early," Moore said. "It was great. It looked they were mad tonight."
The Yankees swept a doubleheader Wednesday, on the way to winning the division, but Bartolo Colon was pounded and New York committed four errors in the finale of this series. Colon (8-10) gave up seven hits and seven runs -- five earned -- over three innings. He's winless in his last nine appearances (0-4).
"It's location, it's movement," Yankees manager Joe Girardi said of the reason for Colon's struggles. "It's some velocity as well. That's why there's concerns. You keep going forward and continue to evaluate."
Andruw Jones smacked a two-run homer and knocked in three for the Yankees, who fell behind 13-0 through five innings but made things somewhat interesting in the eighth.
A throwing error on second baseman Elliot Johnson allowed Chris Dickerson and Eduardo Nunez to score, pulling the hosts within seven runs. Jake McGee, Tampa Bay's third pitcher of the inning, fanned Jorge Posada with the bases full to end the frame.
The Rays loaded the bases with nobody out in the first during a wild inning for Colon, when he hit Upton with a pitch and walked Evan Longoria. Joyce grounded a single into right field for a 2-0 lead. Damon then lifted a sacrifice fly to left field.
Upton hit an RBI triple in the second and scored on Longoria's double.
Zobrist homered to right with Damon aboard in the third, and the fourth saw more long distance shots. Upton and Damon each belted two-run homers and Reid Brignac's base hit plated Zobrist for a 12-0 cushion.
Upton scored on a Zobrist sac fly in the fifth before Jones homered in the sixth. Ramiro Pena and Jones each had RBI singles and Jesus Montero a two-run double in the New York seventh.
Dellin Betances hit Joyce with the bases full in the eighth and Russ Canzler added a sacrifice fly.
The Yanks have won nine of their 15 meetings with the Rays this season...The Yankees used a total of 16 different pitchers (of 19 total arms on the roster) during this four-game series...Pena snapped an 0-for-28 with his sixth-inning single...Betances and Andrew Brackman made their major league debuts on the mound for the Yankees...Moore's 11 strikeouts marked the most by a Rays pitcher in his first career start.