Cincinnati relievers lead the NL in bullpen ERA (2.63) and opponents' batting average (.205), while ranking second in strikeouts (211, to Colorado's 228) entering Sunday.
They have not allowed an earned run through four innings this weekend in New York.
"Their bullpen's deep," said Mets manager Terry Collins. "You see what it's like at the end of the games, especially for us. They've got those two good lefties down there at the end of a game, and when you're behind, it puts us behind the eight-ball for sure."
Chapman has a 1.06 ERA and eight saves on the year, striking out 59 in 34 innings. Sean Marshall (eight), Jose Arredondo (one) and Logan Andrusek (two) also have saves this season.
"Our bullpen has been doing so good that, once you're out of the game, you're feeling pretty confident they're gonna lock it down," said right-hander Homer Bailey.
Each of the relievers on Cincinnati's current roster have an ERA of 3.33 or less, and four have an ERA of 2.70 or less.