Forsberg has 11 points (seven goals, four assists) during the streak.
Justus Annunen made 16 saves for the Predators (15-16-4), who were coming off a 5-3 win against the Toronto Maple Leafs on Saturday and are 7-3-0 in December.
Jonathan Quick made 30 saves for the Rangers (18-16-4), who had won two in a row, including 5-4 in a shootout against the Philadelphia Flyers on Saturday.
Forsberg gave the Predators a 1-0 lead at 10:44 of the second period, roofing a wrist shot over Quick’s glove from the right circle off a nifty pass from Ryan O’Reilly.
O’Reilly has eight points (one goal, seven assists) during a seven-game point streak.
Steven Stamkos scored an empty-net goal from center ice to make it 2-0 at 19:12 of the third period.
Jonny Brodzinski scored 12 seconds later on the rebound of his own shot from the slot to cut it to 2-1.