Semyon Varlamov made 33 saves before turning aside the only two attempts he saw in the shootout, sending the Avalanche to their third straight win. It was Colorado's 30th victory of the season.
O'Reilly deflected a shot past Cory Schneider midway through the first period and Colorado held a 1-0 lead until Reid Boucher scored 8:59 into the third.
New Jersey suffered its 11th overtime loss of the season, tying the Devils with Chicago for most in the NHL.
Schneider made 37 saves for the Devils.