BALTIMORE -- Chris Tillman could not hold a seven-run lead in his last start. He fared better when the Orioles gave him an eight-run edge on Sunday night.

Chris Davis, Travis Snider and Chris Parmelee all homered in a six-run fourth inning, and starter Tillman threw seven shutout innings as the Baltimore Orioles completed a sweep of the doubleheader versus Cleveland with an 8-0 victory over the Indians.

Tampa Bay and the Yankees both lost on Sunday so the sweep of this split doubleheader -- the Orioles scored a 4-0 victory earlier in the day -- lets Baltimore (41-34) pull into a virtual tie for first place with the Rays (42-35) in the American League East. The Orioles (.547) actually lead Tampa Bay (.545) by two percentage points.

In addition, the Orioles won the season series (5-1) against the Indians for the first time in nine years. Also, according to STATS, LLC, this is the first time the Orioles have posted two shutouts in a doubleheader since Sept. 6, 1974 -- also versus the Indians.

Tillman (6-7) now has won four straight decisions, punctuated by a no-decision last Sunday versus the Blue Jays, where he gave up six runs in 1 1/3 innings. The Orioles gave him a 7-0 lead in that game that he could not keep.

This time, he gave up just four hits and struck out six in seven innings. Tillman has struggled with control and command at times this year but did not walk a batter as the Indians (33-41) rarely threatened.

"I've been there so many times," he said. "You sit in the dugout so long, and you've got to go out and make pitches right away. I wasn't capable of doing that last time. It was good to be able to do it this time."

The second victory pushed the Orioles back to the top spot by percentage points but there wasn't much conversation about it.

"The only thing I look at is the loss column every now and then," Orioles manager Buck Showalter said. "I don't pay much attention to the other part of it. See if you can stay engaged and roll the dice in September. That's what it's about."

The six-run fourth inning -- powered by solo homers from right fielder Davis, left fielder Snider and a two-run shot from first baseman Parmelee -- gave Tillman the early eight-run lead, and that proved to be plenty.

Right-hander Toru Murata (0-1) made his major league debut for the Indians (33-41) and looked good at times but the Orioles got to him for five runs on four hits in 3 1/3 innings.

"He got through it the first time," Indians manager Terry Francona said. "The second time through ... he left some balls up. That hurt him. I thought he had very good poise. I love the way he was out there [and] enjoying, competing."

Orioles second baseman Ryan Flaherty got a two-run single in the second before the three-home run fourth. Murata gave up two of the homers and left with the Orioles up, 4-0.

The Indians finished with eight hits, four of which came in the last two innings against left-hander T.J. McFarland. Left fielder David Murphy went 4-for-4, all singles.

Also, Francona was thrown out in the top of the ninth by home plate umpire Ron Kulpa after arguing balls and strikes.

Baltimore took an early lead in Game 2 thanks to a two-out error from Jason Kipnis. The Cleveland second baseman couldn't come up with Snider's hard grounder, and that kept the inning alive.

Shortstop J.J. Hardy sent Snider to third with a double to right. Flaherty followed with his two-run single for a 2-0 lead.

The Orioles broke it open in the fourth when they belted three homers en route to their six-run inning and an 8-0 lead.

Davis started things with a lead-off homer against Murata, which Snider duplicated two batters later to give the Orioles a 4-0 lead. Murata's night ended after he followed that with a walk of Hardy.

Later in the inning, former Oriole Ryan Webb then entered to face Manny Machado, and the third baseman ripped the right-hander's first pitch down the line in left for a two-run double and a 6-0 lead.

Parmelee followed with his two-run homer that gave the Orioles the eight-run cushion, which led to a very quiet Cleveland clubhouse afterward.

"I feel like we just need to get it back in the saddle," Indians center fielder Michael Bourn said. "We just have to continue to play hard, get things clicking right and that's about it."

NOTES: The victory in the first game of Sunday's doubleheader was the 5,000th for the Orioles since the team moved to Baltimore from St. Louis for the 1954 season. ... The Orioles recalled LHP T.J. McFarland from Triple-A Norfolk to use as their 26th player in the second game of this doubleheader. He was returned to Norfolk after the game. ... Indians 2B Jason Kipnis saw his 20-game hitting streak, the longest in the major leagues this year, come to an end in Game 1. He went 0-for-4 in the 4-0 loss. ... The Indians announced before the second game that they released RHP Scott Atchison, whom they designated for assignment on June 23.