Luke Kunin also scored twice, Josi had three assists, and Juuse Saros made 40 saves for the Predators (24-11-2), who have won five straight and are 12-1-1 in their past 14.
Cale Makar had a goal and two assists, Nazem Kadri had two assists, and Darcy Kuemper made 27 saves for the Avalanche (22-8-3), who had won five in a row and are 10-1-1 in their past 12 (both losses at Nashville).
"Obviously, we didn't get the one point that we wanted, but at the end of the day, we still battled back again," Makar said. "It's not an ideal scenario for us having to come from behind every single night (trailed in each of the past seven games), but we're confident in the abilities that we have as a team."