They became the second team to sweep their respective series after the Carolina Hurricanes did the same against the Ottawa Senators on Saturday.
This now marks the Avs' six sweep out of eight playoff series in which they led 3-0 since relocating to Denver in 1995-1996.
Avs goaltender Scott Wedgewood did not allow more than two goals in a game all series and only allowed one goal in three of the four (five total goals).
They now await the winner between the Dallas Stars and Minnesota Wild, which is tied up 2-2 following the Wild's overtime win on Saturday.
Kopitar received one last standing ovation from the Kings faithful in the final two minutes of the game, breaking out into "Thank you, Kopi!" chants as time expired.
Recap & Highlights
After the Avs failed to score on the game's first power play, they made sure not to waste a second opportunity.
Nathan MacKinnon, the NHL's leader in goals scored, found the net for the first time these playoffs to put the Avs up 1-0.
It marked his 56th career playoff goal, needing just three more to surpass Avs legend Peter Forsberg for the second most all-time.
Gabriel Landeskog also picked up his first assist of the playoffs.
Both teams had two power plays each in the first period, with the Kings not being able to capitalize. Colorado outshot LA 11-7, but were outhit 16-5.
In the second period, Colorado would double their lead with an early goal.
Cale Makar scored his second of the series as the Avs went up 2-0 almost six minutes into the second.
His 24th career playoff goal places him just one behind Scott Niedermayer (25) for the 17th most all-time by a defenseman.
It also marked his fourth goal in a potential series-clinching game, surpassing Sandis Ozolinsh for most in Avs history.
But the Kings would try to fight back later in the second.
Joel Edmundson scored his first goal of the postseason off Adrian Kempe's first assist and Alex Laferriere's fourth to make it 2-1.
After a first period that saw a combined seven penalties, neither team committed a single one in the second.
Heading into the third, the Avs would get on the board early to take a two-goal lead yet again.
This time around, it was Nicolas Roy, who scored his second of the playoffs to make it 3-1.
Shortly after the Avs doubled their lead, Brock Nelson would get rung up on a two-minute minor for hooking, giving the Kings a golden opportunity to cut the lead.
But no dice. LA was 3-for-13 on the power play heading into Game 4, scoring once in each of the previous three games.
Then, the Avs made it impossible for a rally en route to their series sweep after Devon Toews put them up 4-1 with his first goal of the series.
Assists came from MacKinnon (2) and Landeskog (2), who recorded his 45th playoff career assist, needing just three more to leap Ozolinsh for seventh-most all time in Avs history.
MacKinnon would score his second of the game (empty-netter) with 5:38 left to go in the game to make it 5-1.
The Kings wouldn't let the Avs go into the second round without some bruises, outhitting them 50-21 in the final game of the series.
Meanwhile, the Avs finished the game outshooting the Kings 32-25 in what would be Kopitar's final game of his incredible 20-year career.
The loss to the Avs made it five straight seasons in which the Kings were eliminated from the playoffs in the first round. They have not made it past the first round in their seven playoff appearances since winning the 2013-2014 Stanley Cup Finals.
