ST. PETERSBURG, Fla. -- Rays shortstop Nick Franklin hasn't had many moments to remember this season, but pressed into duty after an injury to starter Asdrubal Cabrera, he stepped up in a big way Tuesday night.

Franklin's two-run home run in the sixth inning put the Rays ahead, and Tampa Bay pulled away to a 6-3 win over the New York Yankees at Tropicana Field.

Franklin, who came into the night batting just .133, went deep off Yankees reliever Nick Rumbelow for his second home run of the season. The homer turned a 3-2 deficit into a 4-3 Rays lead.

"He left a pitch over the middle of the plate and I was able to take advantage of his mistake," said Franklin, who spent most of this season at Triple-A Durham. "I didn't mean to get overexcited, but instincts took over, we're down by one. ... Just trying to make the most of it."

Tampa Bay got a quality start from right-hander Jake Odorizzi, who gave up three hits and three runs in six innings. The Rays bullpen backed Odorizzi (8-8) with three innings of shutout relief.

Right-hander Brandon Gomes pitched the ninth for his first career save, becoming the eighth Tampa Bay pitcher to earn a save this season.

The Rays, who piled up 13 hits, added to their lead with two outs in the eighth when Yankees right fielder Rico Noel couldn't make a diving grab on a line drive from Rays catcher J.P. Arencibia. The single knocked in the game's final two runs.

"J.P. Arencibia continues to get big hits with guys on base," Rays manager Kevin Cash said of his No. 9 hitter, who went 2-for-3 to raise his average to .364 as a late-season callup.

New York got a two-out single in the ninth from pinch hitter Dustin Ackley, and then center fielder Jacoby Ellsbury reached on an error, bringing the tying run to the plate. Gomes got left fielder Brett Gardner to pop up to left field for the final out.

The Yankees (79-65) remain three games back of Toronto for the American League East lead, unable to capitalize on the Blue Jays' loss to the Atlanta Braves.

"It's tough that we're not able to hold them down," Yankees manager Joe Girardi said of the missed opportunity. "(Odorizzi) has been pretty tough on us ... we just didn't have a lot of hits."

The Rays (70-74) ended a three-game losing streak. They scored one run in the previous two games and went a combined 0-for-12 with runners in scoring position in the previous three.

Franklin's home run came after the Yankees took a 3-2 lead on a two-run homer from rookie first baseman Greg Bird in the fourth inning.

The teams traded leads three times early in the game, with the Yankees jumping ahead in the first on designated hitter Alex Rodriguez's 32nd home run of the season, a solo shot to right field off Odorizzi.

The Rays tied the game in the bottom of the first with four hits off Yankees starter Adam Warren, with second baseman Logan Forsythe getting an RBI single to drive in left fielder Grady Sizemore, who had singled.

Rays rookie right fielder Mikie Mahtook tied the game in the second, hitting a leadoff double, stealing third and coming home when the throw from catcher Brian McCann got away from third baseman Chase Headley for a fielding error and a 2-1 lead.

Warren lasted only four innings. He allowed two runs on six hits.

"I feel like it's coming around and it's just a matter of time," said outfielder Jacoby Ellsbury, stuck in an 0-for-25 slump. "(I) could at any point now get some results."

Rays shortstop Asdrubal Cabrera left the game after four innings with a left knee strain, and the Rays said he is day-to-day. Franklin replaced him in the fifth and committed an error on his first chance.

NOTES: Yankees DH Alex Rodriguez had an MRI on his right knee that showed it was only a bone bruise, and he not only batted third as the team's designated hitter Tuesday, he crushed a solo home run in the first inning, his 32nd of the season. ... Thursday is Roberto Clemente Day, and the Rays staff and players will wear T-shirts to commemorate the day -- fans who donate a canned food item can receive the T-shirt as well. ... Tampa Bay is 2-13 in extra innings this season, including 11 consecutive extra-inning losses, a club record. Per Elias, the only longer extra-innings losing streaks in major league history were 13 games, for the 1969-70 Montreal Expos and the 1906-07 St. Louis Cardinals.