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Los Angeles forced overtime with three goals in the third period.
Los Angeles was up 5-0 late in the second period before Auston Matthews scored on his first career penalty shot.
Tanner Pearson and Dustin Brown scored for the Kings, who had their three-game winning streak snapped and fell to 9-2-1.
Tyler Toffoli scored off a faceoff — his second goal of the game — just before time expired in overtime to give the Los Angeles Kings a 2-1 win over the Boston Bruins on Saturday night.
It was Quick's second shutout this season and came in his 500th career game.
Kempe also scored the shootout winner as the Kings edged Ottawa 3-2 on Tuesday night.
Adrian Kempe and Trevor Lewis scored for Los Angeles (6-1-1), which had won four in a row.
At 6-0-1, Los Angeles is off to the best start in franchise history.
Anze Kopitar had a goal and an assist, leading the Los Angeles Kings to a 3-2 victory over the New York Islanders on Sunday night.
Drew Doughty scored the tiebreaking goal on a power play with two minutes left in the Los Angeles Kings' 4-2 victory over the winless Buffalo Sabres on Saturday night.
Dustin Brown scored the tying and go-ahead goals on artful deflections early in the third period for the Kings, who lost for the first time under new coach John Stevens.
Jonathan Quick stopped 24 of 25 shots to earn the victory for the Kings, who won their road opener for first-year coach John Stevens.
LA Kings employee Christiana Duarte was one of the many victims of the Las Vegas shooting remembered Thursday night before the game.
Trevor Lewis and Tyler Toffoli scored for the Kings, who immediately got a vintage game from their well-rested goalie.
