Viktor Arvidsson, Mike Fisher and Kevin Fiala also scored, and Roman Josi had two assists for the Predators.
Pekka Rinne stopped 37 shots, improving to 17-7-2 in his career against the Avalanche. He also finished the month 9-1-2.
Johansen and Watson scored in the first 2:42 of the third period to put Nashville up 5-2. The Predators have won eight of 11.
Mikko Rantanen and Rene Bourque each had a goal and an assist, and Mikhail Grigorenko also scored for Colorado, which has started a five-game homestand 0-2-1.