Dvorak, who also won 14 of 17 face-offs, has 19 points (seven goals, 12 assists) in 28 games, more than halfway to the 33 points (12 goals, 21 assists) he had in 82 games last season with the Montreal Canadiens.
He signed a one-year, $5.4 million contract with the Flyers on July 1.
"He was more in a defensive role in Montreal, more on the fourth line," Flyers coach Rick Tocchet said. "And I think he's getting a chance. He saw the opportunity here with our situation and I think that he's grabbing it."
Konecny said having Dvorak as the center between him and Zegras has allowed them to play a bit freer.
"He's that guy that, unfortunately, sometimes when you're playing with myself or 'Z,' we're leaning offense sometimes, and he seems to be a guy that's going to be in the right spots," Konecny said. "If there's a mistake, we don't want that, but he's got the mindset of protecting and cleaning up a lot of errors that I'm making. He's also got a lot of [offense] too, so I think he's all around a really good player and I've enjoyed playing with him."
Konecny had the secondary assist on Dvorak's goal for his 500th NHL point.
"It's awesome. ... But I think for me, where I'm at in my career, those are good, but I just want to be in the (Stanley Cup) Playoffs," Konecny said.
Grundstrom put the Flyers ahead 2-1 at 3:20 of the second period when he deflected Nick Seeler's shot from the blue line. It was Grundstrom's first goal of the season, and came in his first game against his former team -- the Sharks traded Grundstrom to the Flyers on Oct. 5.
"You always want to beat your old team, that's for sure," Grundstrom said. "So it feels really good."
Cates' wrist shot found the back of the net at 19:48 to put the Flyers ahead 3-1. He settled a saucer pass from Bobby Brink on the rush to score from the left face-off circle.