Jonathan Bernier made 32 saves for the defending Stanley Cup champions, who tied it with 9:34 left on Jeff Carter's goal during a two-man advantage. King then made a spinning pass from the boards in front to Kopitar, who beat Jimmy Howard for his sixth goal of the season.
Howard stopped 27 shots for the Red Wings, who had won two straight after an 0-3-2 skid.
Kyle Quincey scored his first goal of the season on a misplay by Bernier in the first period.
I don't have a crystal ball. Predicting is a real complicated thing. If we stay healthy, have enough depth and get the good goaltending we think we're going to have, you can go all the way. But a lot of things have to happen. There's going to be a lot of teams that think the same thing. Everyone made deals. We're all are optimistic about where we'll end up.
— Rangers general manager Glen Sather after being asked if he's constructed a team that can win the Stanley Cup before their 4-1 win against the Predators on Monday