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CLEVELAND -- As the Tampa Bay Rays' regulars wolfed down postgame meals while peaking at an NL afternoon game on the clubhouse TVs, their travel bags were packed and stacked on a cart outside in the hallway, ready for delivery to the airport.

It was time to go home.

The Rays have finished their road work.

James Shields pitched seven strong innings to finally beat Cleveland and the Rays improved baseball's best road record with a 7-4 win on Thursday over Justin Masterson and the Indians, who lost for just the second time in 16 home games.

With 10 wins in their last 11 on the road, the Rays are 13-5 outside Florida's borders. And, after a dreadful 1-8 start, they've gone 21-7.

"By now it's been forgotten," Shields said of the club's horrendous April opening. "We're playing on all cylinders right now."

Shields (4-1) gave up two runs and scattered seven hits, piggybacking off David Price's dominant performance on Wednesday night when Tampa Bay's ace stopped Cleveland's home winning streak at 14. The right-hander came in 0-4 in six career starts against Cleveland, the only AL team he had never beaten.

"I beat Cleveland, at Cleveland," he said, smiling. "I got one more on my bucket list."

Shields improved to 4-0 with 1.12 ERA in his last five starts overall.

Reid Brignac, Sam Fuld and Evan Longoria had two RBIs apiece as the Rays handed Masterson (5-1) his first loss.

By winning two of three, the Rays cooled down the Indians and had some success in a ballpark that has haunted them in recent years. Tampa Bay is just 4-19 in Cleveland since 2005.

"If you're looking for a little bit of a litmus test, there it was," Rays manager Joe Maddon said. "What can I ever complain about? Win or lose the effort is there every day. I just have to sit there and make the right decisions. Our guys came ready to play."

The Indians, on the other hand, are facing their first turbulence this season.

Asdrubal Cabrera homered for Cleveland, but the Indians couldn't string any hits together until it was too late and had two runners picked off by Shields, who caught Michael Brantley at first in the third and Cabrera off second in the sixth.

"We didn't play very well," Indians manager Manny Acta said. "Masterson was behind in the count and struggled with his command. We didn't do enough offensively and we gave away a couple of outs on the bases."

Shields picked up right where Price left off. He took a shutout into the sixth and made big pitches whenever trouble brewed. He walked one and struck out seven.

Cleveland outfielder Grady Sizemore missed his second straight game with a bruised right knee. An MRI exam showed no structural damage, a huge relief to the Indians and Sizemore, who sat out most of 2010 after undergoing microfracture surgery on his other knee.

The Rays didn't have outfielder B.J. Upton. He served the first game of a two-game suspension handed down by Major League Baseball following a tirade after he was ejected on May 4. Upton will also sit out Friday's series opener at home against the Baltimore Orioles.

For the second straight day, Tampa Bay jumped to an early lead on the Indians, who made a habit of scoring quick runs while winning a club-record 18 games in April and building a surprising lead in the AL Central.

The Rays scored four in the second off Masterson, who was having trouble locating his fastball during a scoreless first inning.

After the Rays loaded the bases on a walk and two singles, Brignac gave them a 2-0 lead with a two-run double, his first extra-base hit in 105 at-bats -- a club record. Brignac had hit nothing but singles since Sept. 22 but slapped a double into the left-field corner.

"He kept his head down so well, he didn't know where the ball was," Maddon said. "Somebody yelled, 'Run, Forrest, run!' and he finally took off."

Brignac could finally joke about his lack of pop.

"It felt so good I didn't even know where the ball was," said Brignac, unaware how long it had been since his last extra-base knock. "When I'm going good I don't want to know my stats, and when I'm going bad I don't want to know them.

"I just know they weren't good," he said.

Cabrera led off the sixth with his sixth homer, a towering shot to right center. Shin-Soo Choo singled and Orlando Cabrera's two-out RBI double pulled the Indians within 5-2. But with the Rays shifting three infielders to the left side with pull-hitting Shelley Duncan up, second baseman Johnson sneaked behind Cabrera and Shields picked him off.

"I don't know if I got him on that or not," Shields said. "The umpire called him out and that stopped the damage right there."

Game notes

Rays outfielder Johnny Damon had two hits, moving him into a tie for 73rd place on the career list with 2,605. Next up for him are No. 72 Jimmie Foxx (2,646) and No. 71 Ted Williams (2,654). ... Young guns: With an average age of 26.3, Cleveland's pitching staff is the majors' youngest. ... Joyce leads the AL with a .358 average. Joyce, Fuld and Jason Bartlett (2009) are the only Tampa players to top the league batting race later than the first week of the season. Fuld was at .366 on April 22.