Kovalev was drafted by the New York Rangers in the first round, 15th overall, of the 1991 NHL Entry Draft. He became the first Russian-born player to be drafted in the first round in the history of the NHL as well as the first Soviet player to be drafted in the first round. Best known for his stickhandling skills, deking ability and wrist shot, he became an important part of the Rangers' 1994 Stanley Cup run, finishing with the third-most points for New York in the 1994 playoffs. Kovalev, Alexander Karpovtsev, Sergei Nemchinov and Sergei Zubov were the first Russians to have their names engraved on the Stanley Cup. The Rangers' Stanley Cup win is well remembered in Europe because of the first Russian names on the Stanley Cup, as MSG Network broadcaster Al Trautwig said in his essay, "Garden of Dreams".