ST. PETERSBURG, Fla. - With Adam Warren making his first start since June 25 and able to go four, maybe five innings, Joe Girardi knew the challenge ahead. "We're going to need a lot of contributions from our bullpen,'' he said Tuesday.

The Yankees got some but not enough. The second of their six relievers gave up a critical two-run homer in the sixth inning, leading to a 6-3 loss to the Rays Tuesday night at Tropicana Field.

It was a particularly stinging defeat considering the Blue Jays' surprising 3-2 loss to the reeling Braves. The Yankees (79-65) stayed three games back in the AL East.

"It's tough, but we [weren't] able to hold them down,'' said Girardi, whose team took a 3-2 lead into the sixth.

Rookie righthander Nick Rumbelow, after escaping a first-and-third, one-out jam in the fifth, was not as fortunate in the sixth. He allowed a leadoff single to Logan Forsythe, then left up a changeup to shortstop Nick Franklin, who an inning earlier replaced injured Asdrubal Cabrera. Franklin's two-run blast made it 4-3.

"It was all dictated by the leadoff hitter getting on,'' said Rumbelow, 1-1 with a 3.95 ERA in 14 appearances. "Today's no different than any other outing for me, it's the same process. I want to get every hitter I face out, and I didn't succeed today.''

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When Rico Noel, who ran for Carlos Beltran in the eighth, failed to come up with J.P. Arencibia's two-out flare to rightfield in the bottom of the inning, two runs scored to make it 6-3.

"It kind of hung up in the lights a little bit,'' Noel said. "But it went in my glove and came out of my glove, I kind of smacked the ground hard.''

Those eighth-inning runs were charged to Bryan Mitchell, whom Girardi called on instead of Dellin Betances. "He's been used so much,'' he said. "The only way I was going to use him is if we were tied or ahead.''

Rookie Greg Bird gave the Yankees a 3-2 lead in the fourth with his sixth homer. The two-run shot ended a 10-pitch at-bat in which Jake Odorizzi threw him nothing but fastballs.

Alex Rodriguez gave Warren a lead before he took the mound by hitting his 32nd homer, his sixth in 11 games. A-Rod has a bone bruise on his left knee that was diagnosed Tuesday, and Girardi said the DH is doing OK.

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But besides the two homers, the Yankees, who had five hits, were mostly quiet. Odorizzi (8-8, 3.26) allowed three runs and three hits in six innings.

Enny Romero pitched a scoreless seventh, and Alex Colome pitched a scoreless eighth. With closer Brad Boxberger, who blew the save Monday night, unavailable, Brandon Gomes allowed a two-out, pinch-hit single to Dustin Ackley and Jacoby Ellsbury reached on an error, bringing up Brett Gardner as the potential tying run.

In the seventh, Gardner was robbed of an extra-base hit that would have scored a run on a spectacular catch by centerfielder Kevin Kiermaier. This time, Gardner flied to left to end it.

The Rays (70-74) had four hits in the first but scored only once. Warren, on a pitch count of 65 to 70, allowed two runs and six hits in four innings.

"Body felt great, my arm felt great,'' said Warren, who figured he'll be able to throw 80 pitches in his next start. "I was very pleased how I felt. I was encouraged by that.''