ATLANTA -- The New York Yankees have provided plenty of run support for pitcher Nathan Eovaldi this season, and on Sunday afternoon he needed every bit of it.

Eovaldi, supported by three early home runs, extended his league-leading winning streak to nine games in the Yankees' 20-6 victory over the Atlanta Braves at Turner Field.

Eovaldi (14-2) allowed five runs, the most he's allowed during his winning streak. He pitched five innings and gave up eight hits and two walks, with seven strikeouts.

"His splitter was up today," Yankees manager Joe Girardi said. "That was the biggest problem he had today. He didn't have his command, but he battled through it."

The Yankees, who average 7.06 runs per start for Eovaldi, again provided support for the right-hander.

Center fielder Jacoby Ellsbury, third baseman Chase Headley and second baseman Stephen Drew each went deep over a two-inning span to help the Yankees sweep the three-game series and send Atlanta to its 12th loss in 13 games.

With the win, the Yankees remain 1 1/2 games behind Toronto in the American League East.

It marked the 12th time this season the Yankees have scored double-digit runs, and the second time this series. The 38 runs are the most scored by New York in a three-game series this year, and the most since they got 41 against Baltimore in May 2004. The 20 runs Sunday were not a single-game mark; the Yankees scored 21 against Texas on July 28. It was the most runs the Braves allowed in a three-game series since they came to Atlanta in 1966.

"The big thing is we got guys swinging the bats here," Girardi said.

Atlanta starter Julio Teheran (9-7) was roughed up for eight runs on nine hits over 5 1/3 innings and left with the bases loaded. He walked three and struck out four and suffered his first loss in August. The eight runs matched a season high; he also allowed eight runs against the Dodgers on April 26.

"He'd rattled off some pretty good games," Braves manager Fredi Gonzalez said. "I think the residue of the first couple games took over."

Teheran, making his first career start against the Yankees, entered the game with a 7-1 record at home. He is now 0-3 against American League teams this season.

Ellsbury hit a 3-2 pitch from Teheran into the seats in right field for a three-run homer in the second inning. It was his seventh homer and sixth over his last 41 games.

The Yankees hit a pair of homers in the third inning. Headley hit a two-run shot to center field, his 10th, and Drew hit a towering two-run homer, his 16th, that just stayed inside the foul pole in right field.

Headley was 3-for-3 with a double, a homer, four RBIs and three runs scored. Drew was 4-for-4 -- pushing his batting average to .201 -- with a homer, two walks, four RBIs and four runs scored.

Atlanta scored twice in the third inning with a two-out rally. First baseman Freddie Freeman drove in a run with an opposite-field single, and catcher A.J. Pierzynski also went the other way with an RBI single.

The Braves chased Eovaldi in the sixth inning when they batted around and scored three times. Eovaldi allowed the first three runners to reach, the last on a two-run single by shortstop Andrelton Simmons.

Pinch hitter Jonny Gomes looped an opposite-field single against reliever Adam Warren to drive in a run and cut the lead to 8-5. Atlanta loaded the bases, but lefty Chasen Shreve retired Pierzynski on an easy grounder to first base.

"We get back to within three runs and that put us close and they put up a big number," Gonzalez said. "It's difficult, it's demoralizing. They'll keep grinding like they have all year and we'll keep trying to figure it out."

That's when the bottom dropped out for Atlanta. The Yankees sent 14 men to the plate in the seventh inning and scored nine runs. Catcher Brian McCann, Headley and pinch hitter Alex Rodriguez each drove in two runs during the inning.

The Yankees batted around again in the eighth and scored three more times. One of the RBIs came from relief pitcher Branden Pinder, who doubled for his first career hit.

NOTES: New York 1B Mark Teixeira missed his third straight start because of bone bruise in his lower right leg. ... The Braves have not yet announced their starting pitcher for Wednesday's game in Miami. It is the spot normally taken by RHP Williams Perez, but he was optioned to Triple-A Gwinnett on Saturday. ... Atlanta starts a three-game series against the Marlins on Monday, while New York opens a three-game series in Boston. Atlanta will send rookie RHP Mike Foltynewicz (4-6, 5.71 ERA) vs. Miami LHP Chris Narveson (1-1, 7.04 ERA). New York RHP Ivan Nova (5-6, 4.50 ERA) will be opposed by Boston LHP Eduardo Rodriguez (7-5, 4.39 ERA) in the first game.