Ryan O'Reilly's shorthanded goal 45 seconds into overtime capped Colorado's rally from a two-goal deficit in the third period at Pepsi Center.
O'Reilly spun around a defender near the net before beating Martin Jones with a backhander for the winner.
"That looked like a Peter [Forsberg] move for sure," coach Patrick Roy said.
Dwight King's power-play goal 38 seconds into the third period put L.A. up 3-1. But Steve Downie roofed a power-play goal at 3:20 and O'Reilly forced overtime by pumping his own rebound behind Martin Jones.
Colorado's Andre Benoit beat Ben Scrivens 26 seconds after the opening faceoff to give the Avalanche a quick lead. Justin Williams' power-play goal 25 seconds later got the Kings even, and Los Angeles went in front at 3:10 when Denver native Nick Shore one-timed Williams' pass behind Slava Voynov.
It was Colorado's first victory under Roy, who was hired as coach this summer.
"Our guys really want our fans to be proud of this team," Roy said.
|Andre Benoit (1) Wrist shot - ASST: Ryan O'Reilly (1), Matt Duchene (1)|
1 - 0 COL
|PPG - Justin Williams (1) Wrist shot - ASST: Slava Voynov (1)|
1 - 1 Tie
|Nick Shore (1) Wrist shot - ASST: Justin Williams (1), Dwight King (1)|
2 - 1 LAK
|PPG - Dwight King (1) Wrist shot - ASST: Nick Shore (1), Slava Voynov (2)|
3 - 1 LAK
|PPG - Steve Downie (1) Wrist shot - ASST: Matt Duchene (2), Tyson Barrie (1)|
3 - 2 LAK
|Ryan O'Reilly (1) Wrist shot - ASST: Matt Duchene (3), Chris Bigras (1)|
3 - 3 Tie
|SHG - Ryan O'Reilly (2) Wrist shot - ASST: Nick Holden (1)|
4 - 3 COL
|Gabriel Landeskog Holding the stick - 2 min against Nick Shore|
|Jeff Schultz Hooking - 2 min against Paul Carey|
|Paul Stastny Holding - 2 min against Colin Fraser|
|Nick Holden Cross checking - 2 min against Tanner Pearson|
|Dwight King Tripping - 2 min against Tyson Barrie|
|Linden Vey Tripping - 2 min against Steve Downie|
|Nick Shore Too many men/ice - bench - 2 min|
|Andre Benoit Tripping - 2 min against Tanner Pearson|
|Jordan Nolan Too many men/ice - bench - 2 min|
|Linden Vey Hooking - 2 min against Tyson Barrie|
|Paul Stastny Tripping - 2 min against Jake Muzzin|
|Colin Fraser Roughing - 2 min against Steve Downie|
|Steve Downie Roughing - 2 min against Colin Fraser|
|Andy Andreoff Roughing - 2 min against Tyson Barrie|
|Andre Benoit Elbowing - 2 min against Kyle Clifford|