Quick stopped 25 shots in the Kings' home opener, but the star goalie also misplayed McDonagh's harmless cleared puck from deep in the New York end early in the third period, knocking it into his own net.
Henrik Lundqvist made 28 saves, and Rick Nash assisted on both of Richards' goals for the Rangers, who are opening the season on a nine-game road trip.
Jake Muzzin scored for the Kings, who have scored just six goals in three games this season.
This team has been a real treat to say you've been the head coach of them. I'm extremely proud of this group ... after the disappointment of (the Game 6 loss) is digested, it's always a lot easier as a coach when your team has emptied its tank, and that team emptied its tank for me for three months.
— Senators coach Dave Cameron after getting eliminated in the first round by the Canadiens