ST. PETERSBURG, Fla. -- Mike Aviles' solo home run in the 10th inning Thursday gave the Cleveland Indians a 5-4 win over the Tampa Bay Rays, but the four-game sweep was all about dominating pitching for the Indians at Tropicana Field.

After Indians pitchers took perfect games into the sixth inning three games in a row, right-hander Corey Kluber gave up three hits in the first inning Thursday but settled down to strike out 14. That was part of Cleveland's 19 strikeouts, most ever for a Rays opponent.

"Man, he buckled down and threw the ball so well," Indians manager Terry Francona said. "We held our ground and gave ourselves a chance to win, and that's hard to win on the road in an extra-inning game."

The Indians (37-41) completed a four-game sweep of the Rays (42-39), who hadn't been swept in a four-game series since September 2009 at the New York Yankees.

The Rays have dropped nine of 11 games and fallen out of first in the American League East. The bullpen gave up runs in all four losses to Cleveland.

"We ran into a little bit of a hot pitching staff, with some really good performances on their end," manager Kevin Cash said. "To give up the home run there in the (10th), that was a tough one to take, but it's part of the game."

Aviles hit the home run -- his fourth of the season -- off reliever Xavier Cedeno (1-1), who took the loss after four Rays relievers had pitched four-plus innings of scoreless relief.

Kluber struck out 14, his second-highest total of the season. He left after eight innings, with the game tied 4-4, having thrown 85 of 115 pitches for strikes.

"Even when they're not getting hits, they're swinging early in the count a lot of times, and I think it's just kind of the way guys generally attack me," Kluber said.

Cody Allen pitched a perfect 10th for the save, striking out the side on 10 pitches, and 10 of the Rays' last 12 outs came by strikeout.

Rays left-hander Matt Moore, who missed nearly 15 months recovering from Tommy John surgery, pitched for the first time since April 2014. Moore started off impressively, retiring the first nine batters as the Rays built a 2-0 lead.

Tampa Bay, which had seen Indians pitchers take perfect games into the sixth inning three days in a row, ended any drama there with three hits in the first inning.

Designated hitter Grady Sizemore's RBI single gave the Rays a 1-0 lead, and a double steal, plus a throwing error by catcher Yan Gomes, allowed third baseman Evan Longoria to score.

Cleveland cut the lead to 2-1 in the fourth on a sacrifice fly by center fielder Michael Brantley, scoring second baseman Jason Kipnis, whose bloop pop to shallow left had dropped in for the team's first hit.

After allowing just two hits in the first four innings, Moore ran into trouble in the fifth. He gave up four hits, including three straight RBI singles by Kipnis, shortstop Francisco Lindor and Brantley. Moore left the game after 4 2/3 innings and 81 pitches, trailing 4-2. Reliever Steve Geltz got out of a bases-loaded jam to keep the Rays within two runs.

"I have to be better than four singles and a walk," Moore said of his fifth inning. "Gotta be able to get out of that inning. ... It was a tough in-game adjustment, but I've got to be better than that."

In the sixth, the Rays struck for four hits, including three with two outs, off Kluber to tie the game. Sizemore had his second RBI single of the game; and, after a single by second baseman Logan Forsythe, the Rays tied the game when shortstop Asdrubal Cabrera hit a single off the glove of first baseman Carlos Santana.

NOTES: The Rays optioned RHP Preston Guilmet to Triple-A Durham after the game, reinstating 1B James Loney from the 60-day disabled list. ... When Carlos Carrasco lost a no-hitter with two outs in the ninth Wednesday, it was the first potential Indians no-hitter to miss by a single out since 1954, when Chicago's Minnie Minoso broke up Early Wynn's no-hitter, according to SABR's Stew Thornley. ... The Rays had six hits in the first three games of the series and ended up with 14. Going back to 1914, the fewest hits for any team in a four-game series is 11, by the 1961 Boston Red Sox. The next lowest total is 13, which has happened eight times. ... The Rays issued fans "Moore 55" stickers to celebrate starter Matt Moore returning to the mound for the first time in nearly 15 months. Moore had Tommy John surgery in April 2014. ... Cleveland held an opponent to three hits or fewer for three games in a row for the first time since 1970. The Indians have held teams to three or fewer hits eight times this season -- only the Rays' pitchers (nine) have done it more.