The defeat, coupled with the Blue Jays' 3-2 loss to the Braves at Turner Field, kept the Yankees three games behind Toronto in the American League East race.
"I don't want to give up runs in any outing," Rumbelow said. "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."
Alex Rodriguez and Greg Bird homered off Odorizzi, who permitted three runs on three hits while striking out five to win his second straight start. Rodriguez slugged a solo shot in the first inning and Bird launched a long two-run homer in the fourth.
MOMENTS THAT MATTERED Franklin's homer: Franklin did not enter the game until the top of the fifth after shortstop Asdrubal Cabrera exited due to a left knee strain, but Franklin managed to make a difference in the bottom of the sixth when he hit a two-run homer off Rumbelow to give the Rays a 4-3 lead. Franklin has spent the bulk of the season at Triple-A Durham. More >
A-Rod, Bird go deep: The Yanks once again produced some big swings against Odorizzi, but weren't able to muster beyond what left the yard. Rodriguez grabbed the team lead with his 32nd homer and Bird launched his sixth career homer in the fourth inning, a two-run blast that pelted the wall deep beyond the center-field fence. According to Statcast™, Bird's blast was projected to have traveled 440 feet and had an exit velocity of 110.7 mph. Rodriguez is playing despite a deep bone bruise in his left knee sustained on Sunday.
"He's been pretty tough on us. When we've gotten to him, we've hit home runs," Yankees manager Joe Girardi said. "That's kind of what we did tonight; we just didn't have a lot of hits. I thought he elevated his fastball well and used his split and other pitches pretty well."
Kiermaier robs Gardner: Rays fans almost feel like they are watching a highlight film that never ends when Kevin Kiermaier robs a hit. "The Outlaw'" did it again Tuesday night when Brett Gardner smoked a ball to deep left-center field with two outs in the seventh and a man on second. Kiermaier tracked down the blast that would have driven home the tying run and made a splendid running grab. According to Statcast™, Kiermaier reached a max speed of 19.6 mph and covered 84 feet on the play.
Didi's bad break: Girardi said that Didi Gregorius erred in breaking for home plate on Gardner's one-out chopper back to the mound in the fifth inning. The Yanks had runners at second and third against Odorizzi, an opportunity that was erased as Gregorius was easily cut down on a fielder's choice and Rodriguez struck out.
"You get used to it and you get spoiled by it, but as soon as you see it off the bat, you're thinking double and then he comes out of nowhere." -- Rays manager Kevin Cash, on Kiermaier's catch in the seventh
"I had to pull up a tad to wait for it to come out of the lights. It went in my glove, it came out of my glove. I smacked the ground hard. I wish I'd have made the play." -- rookie outfielder Rico Noel, on Arencibia's two-run single
SOUND SMART WITH YOUR FRIENDS Brandon Gomes recorded his first career save in his 165th career appearance. In doing so, Gomes became the eighth Rays pitcher to record a save this season.
Cabrera grounded into a 3-6-1, inning-ending double play in the first. The Rays thought Cabrera beat the throw, so they challenged the call. After review, it was ruled that the call stands.
WHAT'S NEXT Yankees:Luis Severino (3-3, 3.35 ERA) will make his eighth career start as the Yankees complete their three-game series with the Rays on Wednesday at 7:10 p.m. ET. Severino will try to bounce back after allowing a career-high six earned runs in his last start vs. the Blue Jays. He defeated the Rays on Sept. 4 with 6 1/3 innings of one-run, seven-hit ball.
Rays:Chris Archer (12-11, 2.95 ERA) will look to improve on his last outing against the Yankees, when he lost to them for the first time in his career after Brian McCann and Rodriguez hit back-to-back home runs at Yankee Stadium on Sept. 6.
Bill Chastain is a reporter for MLB.com. Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch, on Facebook and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.