Kessel opened the scoring in the first period and then added a second-period score that gave the surging Leafs a 4-0 lead.
The victory gave Toronto its longest winning streak since the 2005-2006 season and moved them within six points of first-place Boston in the Atlantic Division.
James Reimer made 35 saves and shut the Avalanche out in the first two periods before giving up two goals to Colorado's Nathan MacKinnon.
Semyon Varlamov allowed two goals on 20 shots before calling it a night early in the second period. Jean-Sebastian Giguere allowed one more goal on 20 shots.