CINCINNATI - The thump of the beat emanated from the center of the clubhouse, leaving even the concrete walls here overmatched. From behind the closed doors, the sounds of a team on the brink of a great achievement came seeping through every opening, music mingling with cheers and, perhaps, a dash of relief.

The Mets had arrived here looking to wipe away the bitterness of a homestand gone wrong, so after beginning their final road trip with a 6-4 win over the Reds Thursday night, they allowed themselves to exhale.

"It was a good ballgame tonight,'' said Daniel Murphy, whose tiebreaking two-out triple in the seventh pushed the Mets to the edge of officially driving a stake into the Nationals. "It was a good win. It put us one step closer."

The Mets shaved their magic number to three -- aided by the Nationals, who blew a late lead in a loss to the Orioles -- and lead the NL East by 71/2 games with nine games to play. With the franchise's first NL East title since 2006 merely a formality now, champagne could be splashed as early as Saturday.

Home-field advantage in the NLDS remains a goal, however, and the Mets trail the Dodgers by 11/2 games. The Mets hold the tiebreaker by virtue of winning the head-to-head matchup.

But that remains a matter for another day, at least to manager Terry Collins, who has barely bothered to hide his emotions. That the chances of a collapse are painfully slim have provided little comfort.

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Yes, the ride has been bumpy, with the Mets going 3-6 before hitting the road, but at no point have they been in imminent danger of ceding the driver's seat in the NL East. Still, Collins has appeared wound up, even tense, despite his insistence that he can "manage the anxiety."

Only victories can take the edge off, which is why this win provided some much-needed therapy for the Mets.

Despite what he called his best fastball command since his return from the disabled list, Long Island lefty Steven Matz offered another mixed bag in his 52/3 innings. He tied a career high with eight strikeouts and walked none but allowed 10 hits, which got louder as the game went on.

Working with a 3-1 lead, Matz allowed the Reds to chip away. Brandon Phillips ripped a breaking pitch to left for a run-scoring single in the fifth, cutting the Reds' deficit to one run before Todd Frazier's long fly ball to left died at the warning track.

Back out for the sixth, Matz didn't survive to see the end of the frame, victimized by Adam Duvall's pinch-hit single on a one-hopper that skipped past third baseman David Wright.

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But the Mets regained control with a three-run seventh. After Murphy's triple down the rightfield line, Yoenis Cespedes had a run-scoring single and Lucas Duda added an RBI double.

Murphy is hitting .461 in his last seven games. "He's locked in," Collins said. "We've seen it for six years. When this guy gets hot, nobody can get him out.''

Hansel Robles allowed a homer by Jay Bruce in the eighth after surviving another controversy. His quick pitch to Bruce was ruled a ball, prompting Collins to question why it hadn't been called a no pitch. But the point was moot.

Jeurys Familia, fresh off allowing a three-run homer by the Braves' Freddie Freeman the night before, bounced back with a 1-2-3 ninth for his 42nd save, one shy of tying the club record held by Armando Benitez.

At one point during their homestand, the Mets had to be reminded to inject life into their clubhouse. They had to be told to blast the music. This time no reminders were needed.

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The walls shook. The beat played on. And the Mets moved to within arm's reach of ending years of darkness.

"It's fun," said Murphy, who has weathered many of those dismal days. "That's the easiest way to describe it. You don't need a lot of adjectives."