In 1996–97, Konstantinov helped his team to win the Stanley Cup against the Philadelphia Flyers. Flyers head coach Terry Murray expected his top line of centre Eric Lindros, left winger John LeClair and right winger Mikael Renberg—known as the "Legion of Doom" for its scoring and toughness—to face Konstantinov. However, Red Wings head coach Scotty Bowman surprised the Flyers by instead opting for the finesse-oriented defense pairing of Nicklas Lidström and Larry Murphy to neutralize the Lindros line's forechecking. In that same year, Konstantinov was runner-up to Brian Leetch for the James Norris Memorial Trophy, given to the NHL's best defenseman. This would turn out to be Konstantinov's final season.