Richards' power-play goal at 8:29 of the third period made it 2-0 and proved to be the game-winner. The Rangers had the man advantage after Cody Hodgson was called for tripping Rick Nash following his breakaway chance that was stopped by Rangers goalie Henrik Lundqvist.
Hodgson tried to slip the puck by on the backhand, but Lundqvist came up with a quick leg save to keep the Sabres scoreless.
"That's a perfect scenario for a goalie when you stop a breakaway and then we score on the power play," Lundqvist said. "It's a different game if they tie it up. I think it was 1-0 on the first one. I think for a goalie you have to be there when mistakes happen, and it's going to happen, I felt like they were taking more chances also in the third to get going. I knew I had to be ready. It felt really good."
Lundqvist made 27 saves one day after signing a seven-year contract extension reportedly worth $59.5 million.
"It was weird because it was such a big day yesterday, an emotional day for me," he said. "It was a proud moment for me that they want to commit to me and I want to commit to them. At the same time, I couldn't be super happy because you want more wins. That's what really matters."
Richards wound up with the puck to the left of Sabres goalie Ryan Miller and lifted a sharp-angled shot into the net for his eighth of the season and a 2-0 lead.
"I liked how I ended up down on the goal line," Richards said. "We were moving all over the place and making plays. That kind of confuses teams. [Linemate Derick] Brassard made a good job freezing the goalie giving it down to me. I had a good chance to try and roof one there."
Nash opened the scoring at 17:47 of the first period. He skated past Sabres defenseman Tyler Myers and broke in on Miller. Nash used a deke to get Miller moving to the far post and reached back to slip the puck inside the near post for his fifth goal of the season.
"I was just faking the wide pull and hoping he'd bite on the backhand and hopefully there'd be something open there," Nash said.
The goal was the ninth of Nash's career in 14 games against the Sabres. Buffalo has allowed the first goal in 24 of its 29 games.
"I knew he was going to do something like that," Miller said. "I didn't get over quick enough. I should've had it."
Zuccarello made it 3-0 at 14:47 of the third period when he got past defenseman Henrik Tallinder and his wrist shot beat Miller under his glove. It was his fifth goal of the season.
"I thought we had a good performance," Rangers coach Alain Vigneault said. "We were in good shape after the second period. We had some quality chances in the second that could've, I don't want to say put the game away, but might've given us a bit more room there. There were some pressure moments in the game and our big guys came up big."
The Sabres spoiled Lundqvist's shutout with 2:06 to play when Tyler Ennis scored his fifth goal of the season.
"He made some really big saves," Vigneault said. "He's an elite goaltender that comes up big at the right time and certainly helped us win tonight."
Miller made 28 saves for Buffalo, now a League-worst 6-21-2.
"Same problems. Another day where we've got to search for the answers," Sabres coach Ted Nolan said. "There's no one [who will] ride in here and fix it for us. We have to fix it ourselves. We have to look in the mirror and [find] what we can do to correct this thing and make it better."
The Rangers (15-14-0) host the New Jersey Devils on Saturday. The Sabres go on the road to face the Montreal Canadiens.