Washington Nationals' Adam Eaton, center, high-fives Juan Soto, left, after Brian Dozier, right, as Eaton scored on a double hit by Anthony Rendon during the fourth inning Wednesday. (Derik Hamilton/Associated Press)

As the Citizens Bank Park organist tapped away at “Take Me Out to the Ball Game,” most of the remaining fans rose, stepped into the concrete aisles and headed toward the exits.

The song accompanies the seventh-inning stretch, when everyone rises, shakes out their limbs and sits back down for the finish. But this rendition serenaded a sad and slow exit for the Philadelphia Phillies’ fans, whose team lost, 15-1, to the visiting Washington Nationals on Wednesday night.

The Nationals fell into a 6-1 hole against the Phillies on Tuesday, then scored 24 unanswered runs between the last five innings of that game and the first eight of this one. Washington’s final run came with Phillies outfielder Aaron Altherr on the mound. The Phillies’ only one came in the ninth off Trevor Rosenthal, who recorded his first, second and third outs of the season in his fifth appearance for the Nationals.

Washington has won back-to-back series and improved to 6-5, with all those games coming against the Phillies and New York Mets. That’s a favorable record given their early bullpen issues and the miscues that filled their first week and change. The offense surged. Starter Jeremy Hellickson backed it. The bullpen did not allow a hit in the final three frames, a second consecutive promising performance on the heels of eight discouraging ones.

It was a good way to head home.

“To come out of the first couple weeks after a bit of rough stretch and be 6-5 right now, of course we’d like to be 8-3, but we’ve got a long way to go,” Nationals Manager Dave Martinez said.

“There’s still so much baseball left,” he added. “We joke around all the time among ourselves: What game is this? It’s Game 11.”

Toward the end of last August, when the Nationals were trudging to a disappointing finish, their 2019 schedule dropped, and this 11-game division test was revealed. Yet they couldn’t have known, some seven months ago, how much talent would be poured into these matchups. The Nationals again built a contender. So did the Phillies, so did the Mets, and so did the Atlanta Braves.

In one winter, with a wave of moves, the National League East became baseball’s most competitive division. And Washington found out, right away, just how tight this race may be.

But this game was close only until the first few pitches were thrown. The Nationals jumped on Phillies starter Nick Pivetta. Adam Eaton, Brian Dozier and Anthony Rendon started it with three straight singles, and the first of three first-inning runs came in when Juan Soto walked.

Hellickson then took that three-run advantage and ran with it. The 32-year-old started the year in the bullpen, the odd man out with the team beginning the season with a four-man rotation. But this game was his, and he threw six scoreless innings while giving up just three hits on 100 pitches.

In his only other outing of the season, on April 2, Hellickson entered in the eighth and gave up a towering home run to Bryce Harper at Nationals Park. In his first matchup with Harper on Tuesday, he struck him out swinging with an 89-mph fastball. Hellickson soon set down eight straight, from the second to the fifth, and sprinkled in contributions at the plate.

In the first, Hellickson worked an eight-pitch at-bat that ended in a swinging strikeout. In the fourth, he singled up the middle and scored on Rendon’s bases-clearing double. And in the fifth, as the lead stretched, he wheeled from first on a triple from Victor Robles and scored the eighth run of his career.

“Why are you sending me?” Hellickson said, laughing, of what he thought when third base coach Bobby Henley waved him home. “He gave me a little one, so I really wasn’t sure what that meant. I knew Robles was right behind me, so it was fun. But I’ll probably not do that again.”

The Nationals batted around in the seventh, plating five more runs, and built enough of a cushion for Rosenthal to get another chance. He has struggled more than any Washington player, throwing 38 pitches and allowing seven earned runs without recording an out heading into Wednesday.

But then he got that elusive out, on his 48th pitch, by striking out Andrew Knapp. He then walked the bases loaded, gave up a run and finished the inning with three outs to lower his season ERA to 72.00.

That was as encouraging as it could have been, with command issues still mixed in. Tony Sipp, the Nationals’ new lefty specialist, left the game with shoulder soreness in the seventh but didn’t seem worried afterward.

The Nationals’ start has been that way, a bit uneven, any success met by setbacks big and small. The first 10 games included bright flashes of upside, a flood of mistakes and a bullpen that, for the most part, has been unable to control the scoreboard. But in the 11th, on a quiet, crisp night, everything seemed to click.