ST. PETERSBURG, Fla. -- Cody Anderson was not thinking about the perfect game that got away in the seventh inning.

The Cleveland Indians rookie was too excited about his first major-league win, part of a combined three-hitter in the Indians' 7-1 win over the Tampa Bay Rays at Tropicana Field on Monday.

"I was mainly just happy we were ahead," said Anderson, whose two major-league starts have both been dominating outings against the Rays. "I'm just out there trying to win. That's my main focus, to try to help these guys win."

Anderson (1-0) retired the first 19 batters he faced, finally losing the perfect game on a solo home run in the seventh by former Indians star Grady Sizemore, now in just his second game with the Rays.

"You're just trying to battle, put a good swing on the ball," said Sizemore, who has four hits in his first two games with Tampa Bay. "He threw well. I thought we had a few good at-bats, hit some balls hard, but we weren't finding any holes. He was on."

Cleveland (34-41) ended a three-game losing streak, while Tampa Bay (42-36) lost for the fourth time in five games.

Immediately after Sizemore's home run, the Rays had third baseman Evan Longoria at second base after a single and error, and he got to third base as the tying run down 2-1. But Anderson got a pop fly from second baseman Logan Forsythe to end the threat.

Cleveland added five runs in the final two innings.

"That was impressive," Indians manager Terry Francona said. "You want your guys to be prepared and wanting to pitch, and he certainly does all that. He's looking like he's ready to enjoy going out and competing and I really like that a lot."

Anderson threw eight innings of two-hit, one-run ball. The 24-year-old had dominated Tampa Bay in his debut June 21, pitching 7 2/3 scoreless innings in what would end up a 1-0 Cleveland win. Anderson, who opened his career with 13 2/3 scoreless innings, struck out two Monday and didn't walk a batter.

Cleveland got an insurance run in the eighth as catcher Yan Gomes hit a solo home run -- his third of the season -- off reliever Kirby Yates to make it 3-1.

In the ninth, Rays reliever Ronald Belisario threw a wild pitch while issuing an intentional walk, allowing the first of four Cleveland runs in the inning to score, two on wild pitches.

The Indians scored in each of the first two innings, getting an RBI single from left fielder Michael Brantley in the first to drive in second baseman Jason Kipnis, who led off with a double. In the second, Kipnis hit a two-out RBI single to score catcher Yan Gomes, who had doubled.

Beyond those two runs, Rays starter Nathan Karns (4-4) kept Cleveland from scoring, despite giving up nine hits in his six-inning outing. The Indians stranded eight runners against Karns, and they grounded into a double play with the bases loaded to end the fourth inning.

"I thought Karnsy, for not having his very good stuff or his best stuff, he really battled," Rays manager Kevin Cash said. "That game could have been 5-0 in multiple innings. It actually felt like we were down by much more than two throughout the course of that game. He did a nice job of kind of battling out there and made some big pitches when he had to."

Seeing Sizemore, a former Indians All-Star, break up what was nearly the Indians' first no-hitter since Len Barker's perfect game in 1981, Francona said he knows how "special" Sizemore was for Indians fans, but he still didn't want to see him break up such a gem.

NOTES: Rays LHP Matt Moore, recovering from Tommy John surgery, threw a bullpen session before Monday's game. The Rays announced after Monday's game that he will start Thursday's game against Cleveland, his first major league appearance since April 2014. RHP Alex Colome will start Wednesday. ... Tampa Bay RHP Jake Odorizzi (oblique) will make his first rehab start Wednesday for Class A Charlotte. He could return to the Rays' rotation from there, or he may need a second rehab start. ... Cleveland took a pair of shutout losses against Baltimore in a Sunday doubleheader. The Indians were swept in a doubleheader for the first time since 2009, as they posted a 23-7 record in their previous 15 twin bills. Cleveland had not been shut out twice in a doubleheader since 1975 against Boston.