Toffoli also was in a perfect spot when the Flyers mishandled the puck. It bounced straight to Toffoli, who scored a short-handed goal late in the first.
VandeVelde, playing on the fourth line, scored with 43.7 seconds left in the first period for his first goal since 2012, lifting Philadelphia to a 2-1 lead.
He credited his teammates for the go-ahead score.
"Their creativity, their second effort, it’s just huge," he said. "They find ways to get you the puck no matter where you are and that’s what happened."
The Flyers pounded Quick with 20 shots in the first, but faded with seven in the second. Philadelphia’s Ray Emery had 38 saves.
Kings-Flyers has become a must-watch game in Philadelphia following the 2011 trades that sent Richards to Los Angeles and Jeff Carter to Columbus. Carter was traded only months later to Los Angeles and paired with his former Flyers teammate to win Stanley Cups in 2012 and 2014.
While the Flyers acquired Wayne Simmonds and Jakub Voracek in the trades, they missed the playoffs in 2013 and were eliminated in the first round last season.
Simmonds and Raffl are tied for the team lead in goals.
"I’ve been in Philly longer than I was in L.A. I think it’s a bit overstated," Simmonds said. "But it’s nice to play against some former friends."
The debate has raged in Philly since 2011 if the Flyers are better are off without Carter and Richards or if they could have somehow won their first Stanley Cup since 1975 had they kept the duo. Carter and Richards helped the Flyers reach Game 6 of the 2010 Stanley Cup finals against Chicago.
Richards started and was booed in pregame introductions. The Flyers held a Halloween costume party for fans and several haunted the arena with defaced Richards No. 18 jerseys. One face-painted fan dressed as a ghoul in a No. 18 sweater and held a sign that read, "Sorry, Mike, but if you’re not wearing orange and black, you’re dead to us."
He was booed again when he tied the game with his first goal of the season.
Richards and Carter both downplayed their only game this season in Philadelphia.
"I have a lot of memories in here and you can’t help but think about it a little bit," Richards said.
At morning skate, Carter said, no hard feelings.
"It’s all worked out for us," he said. "Couldn’t be happier."
NOTES: The Kings allowed only five goals on their recent six-game homestand.