Watch CBS News
The Kings trailed 2-1 going into the third period.
The Kings got an early jump on the Blues with two goals in just over six minutes into the opening period.
The Kings are finally back to feeling good after losing seven of eight from Nov. 9-24.
Dustin Brown and Anze Kopitar scored 2:10 apart late in the second period to put the Kings ahead.
Trevor Lewis scored in the fourth round of a shootout, and the Los Angeles Kings ended a three-game losing streak with a 2-1 victory over the Anaheim Ducks on Saturday night.
Anze Kopitar and Trevor Lewis scored for the Kings, who have lost three straight and seven of eight.
Tyler Toffoli tipped home a power-play goal early in the third period for the Kings, who have lost six of seven.
William Karlsson scored twice, Maxime Lagace stopped 27 shots and the Vegas Golden Knights beat the Los Angeles Kings 4-2 on Sunday night.
Johnny Brodzinski scored his first NHL goal, and Andy Adreoff scored his first of the season to lead the Los Angeles Kings to a 4-0 win over the Florida Panthers on Saturday.
Drew Doughty had the goal for Los Angeles, which has dropped four straight after opening 11-2-2.
Tanner Pearson scored in the opening minute and Anze Kopitar extended his point streak to nine games with a power-play goal moments later for the Kings.
The Pacific Division-leading Kings are off to a strong start despite the injury absences of goal-scoring veteran Marian Gaborik and top scorer Jeff Carter.
The Kings went ahead in the first period on Brown's redirection of Kopitar's shot for the Kings' sixth power play goal in six games.
Stamkos kept the overall NHL scoring lead with 30 points, but Kucherov is right behind with 29.
Jonathan Quick made 33 saves and got an assist on Shore's game-winner.
