New Jersey's Martin Brodeur and Colorado's Jean-Sebastien Giguere were both perfect in goal through 65 minutes before Kovalchuk finally tallied in the opening round of the shootout. Parise then put a backhander into the net to win it.
Brodeur stopped Milan Hejduk and Peter Mueller in the shootout to earn the 651st win of his career.
Brodeur made 28 saves in his second shutout of the season. He has 118 of them in his 19 NHL seasons.
New Jersey won for the fifth time in six games. Colorado had won three in a row.
Celebrity Families of 2014 [PHOTOS]