NEW YORK -- “We know that we’ve been written off, and we don’t care. We’re going to keep fighting and clawing for every last inch.”

That’s what Phillies manager Gabe Kapler had to say after the Phillies’ 5-0 win over the Mets at Citi Field on Saturday night. The team entered the day with playoff odds below 2 percent according to FanGraphs, and even after the win those odds were still below 5 percent. But they did plenty on Saturday that they hadn’t done in a while -- including winning a game via shutout for the first time since July 24 -- showing what this team can be when everything is clicking.

• Box score

Drew Smyly pitched seven scoreless innings and the bullpen finished off the shutout. Smyly was the first Phillies starter to turn in a scoreless start of seven or more innings since he did so himself on July 30. After allowing 5.7 runs per game in their last three games -- all losses -- the Phillies posted a clean evening.

“Smyly went out today and pitched like he didn’t have a care in the world and like he had something to prove, and went through a really good Mets lineup,” Kapler said.

Multiple times, Kapler mentioned that his team has taken notice of the apparent assumption they won't reach October, and he implied it played a role in Saturday's win.

“I think it’s worth noting that Smyly pitched with a little bit of a chip on his shoulder. I think we all kinda came in with a little bit of a chip on our shoulders, similar emotion happening in the dugout today and throughout the clubhouse,” he said.

It wasn’t just the pitching that succeeded on Saturday. The offense got in a groove, too, especially the top three hitters in the lineup, who combined to go 8-for-15 with five RBIs. On the night, the Phillies went 4-for-14 with runners in scoring position -- still not capitalizing on all opportunities but equaling their hits total with runners in scoring position from the prior two nights combined, when they went 4-for-20.

They scored four runs in the fourth inning to add some padding to their then-one-run lead.

“We talk about having the big inning and how important that is for the success of this club,” Kapler said. “A four-run inning to me is a big inning, and it really changes the mood of the dugout on the other side. We feel it when the team scores four, five, six runs in an inning, it really sucks the life out of the dugout. So we know how important those big innings are.”

Perhaps the biggest moment of the game, though, came in the first inning with Todd Frazier at the plate and the bases loaded for the Mets with two outs. He hit a ball toward deep right-center and right fielder Adam Haseley, playing the position with Bryce Harper out of the lineup with a right hand contusion, made a catch to save what could’ve been a bases-clearing double.

“That was literally the game, probably,” Smyly said. “Things would probably be a lot different right now if that fly ball gets over his head. So, that was a huge momentum swing and I was feeling good the whole night.”

The Mets finished the night 0-for-11 with runners in scoring position, their worst such 0-fer in a game since Aug. 24, 2017. That included two strikeouts and a groundout after the fourth inning began with consecutive Brad Miller errors at third base.

“I think Smyly should be applauded for bailing us out when we didn’t make a couple plays behind him. And I think that’s the greatest feeling in the world for Brad Miller who couldn’t have felt worse -- to have your starting pitcher come and just take care of you like that,” Kapler said. “That’s what being a team is all about, we’ve protected and fought for each other all year, and that was a good indication of how it happens between the lines.”

The NL Wild Card race remains in flux, with the Diamondbacks winning Saturday night, the Brewers defeating the Cubs and the Nationals losing to the Braves. With the Phillies sitting three games out of the second Wild Card spot, both Smyly and Kapler extolled the benefits of continuing to win and letting the rest take care of itself.

“We know that we’re being counted out,” Kapler said. “We understand that that’s the sentiment, and we don’t believe it.”

Next up, they’ll go for a series win in Sunday’s rubber match. It would be the Phillies' first series win in a road set of three or more games since they took two of three in Pittsburgh from July 19-21.