Cincinnati is a season-high 10 games above .500 (37-27) and has won five straight. The Reds lead the Pirates and Cardinals by four games in the National League Central.
Bailey, who kept the Mets to the one run on six hits while striking out three and walking just one, held New York to a 2-for-12 mark with runners in scoring position.
"I don't know if it's physical effort, but you try to get locked in a little more and try to make good pitches, but also try not to do too much," Bailey said. "We were able to get out of a jam in the second and then from then on, we just kind of cruised along."
Aroldis Chapman pitched a scoreless ninth for his eighth save of the season.
Niese surrendered back-to-back singles to Zack Cozart and Wilson Valdez to lead off the game, before the Mets lefty retired Joey Votto and Brandon Phillips. But Bruce hammered Niese's 0-2 offering into the upper deck in right field for a quick 3-0 lead.
"It was kinda like a drop-down curveball-slurve thing -- I don't really know exactly what [Niese] calls it," Bruce said. "But it was a breaking pitch. He made a mistake with it and I didn't miss it."
The Mets got one back in the bottom half of the inning, as Daniel Murphy and David Wright notched back-to-back doubles off Bailey. But New York stranded men on second base in the second and third innings, and a man on third in the sixth.
Cincinnati tacked on its fourth run when Bruce was hit by a pitch from Niese in the fourth and came around to score on an RBI single from Ryan Ludwick.
It was the second night in a row that the teams traded hit batsman -- Lucas Duda was hit by Bailey in the sixth -- after Votto and Wright were each hit in Friday night's contest. No warnings were issued by the umpires in either game.
"Nothing, zero," Baker said of any conspiracy theories. "Guys are going to get hit -- I don't care if you're playing Little League or in the World Series. There's nothing behind it."
Niese left after seven innings, allowing six hits and the four runs while striking out seven and walking one.
"You make a mistake and all of the sudden, it's 3-0," the Mets hurler said. "But that's just the way it went. I had to do my best to keep the tune of the game at that point."
The Mets, who entered Saturday with 19 home victories -- the fifth-highest total in the Majors -- have lost three in a row at Citi Field. The Reds, who continue to build on their best mark of the year, are 6-3-2 in their previous 11 road series.
"Our pitching has been great for us all year, from the starting rotation to the bullpen," Bruce said. "We've started hitting a little better lately and I think we're going to continue to do that. But pitching -- we go as the pitching goes. It's been great. Those guys have done a great job."