TAMPA, Fla. - The Cleveland Indians are feeling a little better about themselves.

Good pitching, timely hitting and the team's first sweep of a four-game road series in more than a year can have that effect.

"Our pitching gave us a chance every night, that's stating the obvious. But I think every game is different," manager Terry Francona said after Corey Kluber struck out 14 and Mike Aviles homered on the first pitch of the 10th inning to give the Indians a 5-4 victory over the Tampa Bay Rays on Thursday.

The series began with Francona holding a team meeting after Cleveland was shut out in both games of a Sunday doubleheader in Baltimore.

Cody Anderson, Danny Salazar and Carlos Carrasco flirted with pitching no-hitters Monday, Tuesday and Wednesday, and Kluber, the 2014 AL Cy Young winner, was dominant for stretches of the finale.

The last time Cleveland swept a four-game series on the road was when it beat Minnesota four in a row to close the 2013 regular season and secure a wild-card playoff berth.

"We needed it. You can't come into a series and get ahead of yourself. We needed to get greedy today," Francona said. "You win three, it's easy to go three out of four. Today, it was a hard one to win, but we have to keep going."

Kluber pitched eight solid innings but remained winless (0-4 over six starts) since May 28. Brian Shaw (1-1) pitched one scoreless inning for the win, and Cody Allen struck out the side in the 10th to earn his 15th save in 16 opportunities.

Tampa Bay fanned a franchise-record 19 times in the game.

Aviles homered off Xavier Cedeno (1-0), extending Tampa Bay's losing streak to five games. Michael Brantley had a RBI single and sacrifice fly for the Indians, who also got run-scoring singles from Jason Kipnis and Francisco Lindor.

"I was just going up there trying to be aggressive," Aviles said.

"Any time you can take a series, it's definitely needed," the Indians outfielder said. "Any time you get a situation where we were able to have four nights of good pitching, you've got to try and take advantage of it."

Matched up against lefty Matt Moore, who was making his first start since undergoing Tommy John surgery in April 2014, Kluber allowed four runs and seven hits. He struck out five of his last six batters.

Kluber settled down after he allowed three straight hits and fell behind 2-0 in the first inning. The Rays didn't have another hit until Kevin Kiermaier doubled off the tip of first baseman Carlos Santana's glove leading off the sixth and scored on Grady Sizemore's second RBI single of the game.

Asdrubal Cabrera's infield single — also off Santana's glove — drove in a second run in the sixth, making it 4-4.

Despite setting a team record for strikeouts, Tampa Bay's offence took a small step forward after being shut down offensively over the first three games of the series, outings which saw Anderson, Salazar and Carrasco take perfect games beyond the fifth inning.

The Rays finished with three hits on Monday, two Tuesday and just one Wednesday, when Carrasco came within one strike of throwing Cleveland's first no-hitter in 34 years when Joey Butler singled on an 0-2 pitch.

In addition to being the first time in franchise history that the Rays were limited to three or fewer hits in three consecutive games, it also was the first time in the majors since the Los Angeles Dodgers did it against the Oakland Athletics in June 2012.

A 17-game winner two years ago, Moore was injured during his second start of 2014 and had surgery performed on his pitching elbow two weeks later. He's the ninth starting pitcher used by the Rays this season, tied for third in the AL and fifth in the majors.

The 26-year-old lefty faced the minimum nine batters over the first three innings before fading quickly.

Kipnis and Lindor began the Cleveland fourth with singles and Brantley followed with his sacrifice fly to cut Tampa Bay's lead to 2-1. The Indians added three runs in the fifth off Moore, who threw three wild pitches and allowed four runs, six hits and two walks over 4 2-3 innings.

"I thought there might have been more nervous body-control type issues, but really it felt normal," said Moore, who threw 81 pitches in his first outing against major league hitters in 451 days.

"A couple pitches got away from him, he yanked a couple change-ups," Rays manager Kevin Cash said. "But I think we all came into it knowing he's not going to be fine-tuned in his first outing."

TRAINER'S ROOM

Rays: 1B James Loney (broken left middle finger) could return Friday. ... OF Desmond Jennings (knee surgery) is pain-free, but has not resumed baseball activities.

UP NEXT

Indians: RHP Trevor Bauer (6-5) will face Pittsburgh RHP Charlie Morton (6-1) in the opener of a three-game interleague series Friday night. Bauer is 2-0 with an 0.82 ERA in three interleague starts this season. Morton is 4-0 with a 1.98 ERA in four home starts.

Rays: RHP Chris Archer (9-5) and New York Yankees RHP Masahiro Tanaka (4-3) are set to pitch in the first of a three-game set Friday night. Archer gave up a career-high three homers against Boston in his previous start Sunday.