Colorado's Ryan Johansen scored twice, Rantanen had a goal and three assists and Cale Makar added a goal and two assists.
Ross Colton also scored, Valeri Nichushkin logged two assists and Alexandar Georgiev stopped 27 shots for the Avalanche.
Cal Clutterbuck led the Islanders with a goal and an assist, while Simon Holmstrom, Kyle Palmieri and Anders Lee also scored.
Byram scored his first goal of the season at the 19:18 mark with a wrist shot through traffic from the high slot.
The Islanders grabbed a power-play goal early in the second period as Kyle Palmieri made it 2-2 at 2:56.
Persons:
Matt Martin, Logan O'Connor, Brad Penner, Nathan Mackinnon, Bowen Byram, Mikko Rantanen, Colorado's Ryan Johansen, Rantanen, Cale Makar, Ross Colton, Valeri Nichushkin, Alexandar Georgiev, Cal Clutterbuck, Simon Holmstrom, Kyle Palmieri, Anders Lee, Noah Dobson, Jean, Gabriel Pageau, Ilya Sorokin, Byram, MacKinnon, Lee, Johansen, Makar, Dobson, Georgiev, Holstrom
Organizations:
New York Islanders, Colorado Avalanche, UBS Arena, Avalanche, Colorado, NHL, Cal, Islanders, New, New York, Thomson
Locations:
, New York, USA, Elmont, New York, Colorado, . New York, Clutterbuck