Golden Knights defenseman Brayden McNabb scored the only goal in the Game 4 win, becoming the fourth player in National Hockey League history to score a series-clinching goal against the team he played for the previous season.
The Golden Knights now await the victor of the San Jose Sharks and Anaheim Ducks in the second round.
It's only the third time in North American pro sports history that a team swept its first playoff series in franchise history.
Goaltender Marc-Andre Fleury will get some much-needed rest after backstopping two shutouts in the series. In the playoffs, the Kings only gave up seven goals, which was less than two per game.
Capitals 3, Blue Jackets 2 (2OT): Lars Eller scored 8:59 into the second overtime, giving visiting Washington the win against Columbus in Game 3 of an Eastern Conference first-round playoff series, though the Blue Jackets still have a 2-1 lead in the best-of-seven series.
"We're sky-high right now", said Brayden McNabb, whose second-period goal proved the series-winner against his former team. "LA put on the pressure on him but he was huge for us". They outshot the Knights 31-21 in the game.
The Kings pulled Quick with 1:05 remaining and had one good chance, but Brown's shot from the slot went just wide of the right side of the net.
Brown also hit the left post with 10 minutes to go in the third, typical of the close calls that Fleury turned away with seeming ease.
Vegas has swept the LA Kings in their very first playoff series. They had a shooting percentage of 2.3% as Fleury made 127 saves on 130 Kings shots. "We can't forget how this feels". Only one team, the Ottawa Senators in 2002, has allowed three goals or fewer in a series that lasted more than four games. Fleury earned his 66th playoff victory, breaking a tie with Dominik Hasek for 11th on the NHL's all-time list among goaltenders.