WASHINGTON — Everything felt familiar to Jeurys Familia, even if his job has changed. Wearing his old gray uniform, No. 27. Warming up in the visitor’s bullpen at Nationals Park. Jogging in from the pen — and eschewing the baseball-cap golf cart offering a lift.

“This was special to me,” he said, “because the Mets have always been special to me.”

Familia, who saved 124 games as a Met (including 43 in 2015 and 51 in ’16) is no longer the closer, a job that now belongs to Edwin Diaz. But he still has closer’s stuff and still has a closer’s mentality even as he settles into the equally critical job as the Mets’ eighth-inning guy, a job he performed well at after being dealt to Oakland last year.

“He’s still the same guy,” Mets manager Mickey Callaway said after handing the ball to Familia with a 2-0 lead in the eighth Thursday, and watching Familia pitch a clean frame, highlighted by getting Anthony Rendon to fly lazily to center as the tying run (after he plunked Adam Eaton with one out).

“He was still one of the best relief pitchers available in the offseason, which is why we wanted to badly to get him,” said Callaway.

And Familia craved a return, beyond the $30 million three-year deal he signed.

“This is the organization that gave me a chance to make all my dreams come true,” said Familia, whose first stint in New York lasted from 2012 through last July 21, when the Mets dealt him to the A’s for two obscure pitchers and some international slot money.

“This is the place I’ve always wanted to be. I love it here. I love this team. And I want to do everything I can to get us back to where we were a few years ago. This was a great first day back.”