Cotter gave the Golden Knights a 4-3 lead on a snap shot after they trailed 3-0 in the second period.
Jonathan Marchessault, Nicolas Roy and Pavel Dorofeyev also scored, and Alex Pietrangelo had two assists for the Golden Knights. Logan Thompson made 31 saves.
Nathan MacKinnon, Ryan Johansen and Valeri Nichushkin scored for the Avalanche, who finished the preseason 2-4-0. Alexandar Georgiev made 22 saves, and Cale Makar and Jonathan Drouin each had two assists.
MacKinnon gave Colorado a 3-0 lead on the power play at 7:04 of the second, but Roy cut it to 3-1 at 8:48.
Dorofeyev made it 3-2 at 5:58 of the third on a wrist shot before Marchessault tied it 3-3 at 12:03.
Johansen put the Avalanche ahead 1-0 at 1:57 of the first period, scoring a power-play goal on a rebound.
Nichushkin extended it 2-0 at 10:51.
