Jeff Carter also scored his 20th goal of the season for Los Angeles, which has lost just once in regulation in Dallas in its last 14 visits (11-1-2) and outshot the Stars 40-15.
Richardson's goal was particularly impressive, since the fourth-liner was playing his first game since Feb. 10 and third of the season overall after sitting out as a healthy scratch the other 32 contests. Jonathan Bernier needed to make just 15 saves for the Kings.
Jamie Benn and Ray Whitney scored for Dallas, which had won both previous meetings between the Pacific Division rivals this season by a combined score of 7-2.
We were thinking about Rich back home, but I thought we did a great job getting mentally ready for this game. We're still in a big playoff push and we found a way to get two points. It's not easy. It hit our guys pretty good [Monday] night. We did a great job as a group.
— Dallas captain Jamie Benn on the Stars' OT victory against the St. Louis Blues the night after Rich Peverley collapsed on the bench