Game 5 is Thursday night in Los Angeles when the Sharks will look to end a streak of four straight wins by the home team in this series.
After falling behind 2-0, the Kings showed some fight in a dominant third period. They got on the scoreboard on a power play when Burns was sent off for boarding Anze Kopitar.
Los Angeles wore down San Jose's penalty killers in the offensive zone and scored when Richards knocked in a rebound of Jeff Carter's shot.
The Kings outshot the Sharks 14-2 in the third period, holding San Jose without a shot for nearly 13 minutes but couldn't get the equalizer against Niemi.
Couture gave the Sharks a 2-0 lead early in the second period, deflecting a point shot by Dan Boyle past Quick while Colin Fraser was in the penalty box for roughing Andrew Desjardins in the offensive zone.
Bruins 2, Rangers 1 • At New York, Daniel Paille snapped a tie with 3:31 left in the third period, and Boston put New York on the brink of elimination with a victory in Game 3 of the Eastern Conference semifinal series.
Boston leads the best-of-seven series 3-0 and can advance to the conference finals as early as Thursday at Madison Square Garden. Only three teams in NHL history have rallied from an 0-3 hole to advance.
The Bruins trailed 1-0 heading into the third, but defenseman Johnny Boychuk tied it at 3:10 of the period with his fourth of the playoffs. The Rangers hadn't lost in regulation when leading after two periods since Feb. 4, 2010.
• Boston 2, N.Y. Rangers 1
Boston leads series 3-0
• San Jose 2, Los Angeles 1
Series tied 2-2
• Pittsburgh at Ottawa, 5:30 p.m., NBCSN
Pittsburgh leads series 2-1