BOSTON -- It was hyped as a big series -- even though it's still only August.

Monday night, the first contest of a four-game set between the Cleveland Indians and Boston Red Sox -- the first of seven regular-season games between the likely postseason entrants, lived up to the billing.

In short, it was a playoff-type atmosphere that came down to the tying run dying on second base in the ninth inning.

Tuesday night, Nathan Eovaldi, who tossed 15 shutout innings in his first two starts with the Red Sox before a rocky road outing, faces rookie Shane Bieber on Tuesday night.

"It's my favorite road city to play in," Michael Brantley said on television after hitting one of three Cleveland home runs in a 5-4 decision. " ... It's a great atmosphere that they (the fans) bring every single time and it's fun to be part of."

Asked what this type of game can mean for a kid such as teammate Greg Allen, who also homered, Brantley said: "It's a little taste of the postseason, especially in the ninth inning like that, adrenaline gets going ... it's fun."

It wasn't fun for the Red Sox, who have lost two straight and seen their lead atop the American League East shrink from 10 1/2 to a still-whopping nine games over the idle New York Yankees. Boston (88-36) has lost three games in a row once this season, in late April.

The Indians spotted the Red Sox three runs but roared back on a home run by each of the three outfielders.

"You look at them, they look like us over there," Red Sox manager Alex Cora said. "Very dynamic, they can hit the ball out of the ballpark, they can come back like we do. You have to earn all 27 outs."

The Indians (72-52) moved to within three games of the Houston Astros for the No. 2 seed in the postseason.

"I think a lot of people are making a big deal of it," Corey Kluber said after earning his 16th win. "We're both leading our division right now, stuff like that, but I think we're kind of taking it as another series.

"There's no guarantee that the two of us will end up playing each other again down the road in the postseason, so ..."

Allen extended his hitting streak to 13 straight games (.383) while Brantley has batted .344 with two homers and 10 RBIs in August.

Rick Porcello gave up the home runs and blamed himself on the third one.

"Not trying to take anything away from him (Allen) but I think even I could have even hit that one pretty hard," he said. "That was not a good pitch and it came at the worst possible time."

Bieber (6-2, 4.37 ERA) is 1-0 with a 3.52 ERA over his last four starts and has 71 strikeouts in 68 innings on the season. He began the season winning his first four decisions and is 2-2 since.

This will be his first appearance against Boston.

Eovaldi (5-4, 3.62 ERA) is 2-1 with a 2.70 ERA lifetime against the Indians, but the current Cleveland roster is batting a cumulative .324 gainst him. Yan Gomes is 4-for-8, Melky Cabrera (who also homered Monday) is 3-for-7 and Yonder Alonso 3-for-10.

Boston's Eduardo Rodriguez (ankle) made his first rehab start Monday night in Double A and the reports were positive. He is due to make one more rehab start, which would likely bring him back after Aug. 31. He would still be eligible for the postseason if he's on the disabled list Sept. 1.