Ian Mitchell brought the Blackhawks to within 2-1 at 16:45 of the third period. He shot blocker side from the high slot off a pass from Max Domi, who dug the puck out from along the side boards.
Chicago then had a power play for the final 23 seconds of regulation, but it couldn't get a shot on net.
"It feels great to contribute offensively, and scoring's always a great feeling in this league," Mitchell said. "So definitely exciting, but I definitely would have liked to get the win as well."
Blackhawks forward Tyler Johnson left the game after the first period because he re-aggravated his left ankle, which has bothered him for much of the season.
Richardson said Johnson is unlikely to make Chicago's upcoming three-game road trip across western Canada, which begins at Vancouver on Tuesday.
"He's going to get checked out tomorrow," Richardson said. "I don't think they think it's as bad as it was before, but obviously re-aggravated. It's frustrating for him and tough for the team.
"I'm not sure what happened tonight. I think [against St. Louis], even at the end of the game, he did something, and today just a little bit worse. Before it gets too [much] worse, we thought that was it for today and make sure we get it checked out properly and take whatever course we have to for him."
Kings forward Alex Turcotte, who was the No. 5 pick of the 2019 NHL Draft, made his season debut after being recalled from Ontario of the American Hockey League on Thursday. Turcotte, a native of Elk Grove, Illinois, had one shot in 8:10 of ice time.
"It is obviously a dream come true," he said. "When they start singing the national anthem, I remember coming to games as a kid, that's kind of what they're known for. I kind of got goosebumps. I was just really excited. I have a lot of friends and family here. I had a lot of fun out there."