Los Angeles won here 3-0 on Monday with Jonathan Quick's 31-save shutout in the first of the two-game set.
The Kings were outshot 36-20 on Wednesday.
"I don't think we had a real good game from the get-go tonight, to tell you the truth," Kings coach Todd McLellan said. "We were slow with the puck, a number of shots missed the net, there were deflected or tipped or fumbled (pucks). We just weren't good with the puck. I didn't think we were near as sharp with the puck as we were two nights ago. Some of that has to do with how St. Louis played. They played better tonight than they did the other night."
Brown gave the Kings a 1-0 lead at 10:24 of the second period with his seventh goal in seven games. Athanasiou made it 2-0 at 16:08.
Sundqvist scored at 18:14 of the third period from the slot on a rebound for the 2-1 final.
"Look, it's frustrating, we're not getting rewarded for some of the work that we're doing, but we can do a little bit more and get some puck luck," Blues defenseman Torey Krug said. "We've got to earn it right now. We've just got to get a little greasier around the nets and make it harder for their defensemen and their goalies and we'll get rewarded for it."
NOTES: Los Angeles defenseman Mikey Anderson was a late scratch due to a lower-body injury and is day to day. ... Brown has nine points (seven goals, two assists) in his past seven games. … The Kings had not allowed a goal in 128:33, dating to the third period of a 4-2 win against the Arizona Coyotes on Saturday. … St. Louis defenseman Marco Scandella left in the third period after being hit in the face with the puck. Berube said he will be reevaluated Thursday. ... The Blues had possession of the puck during a delayed penalty in the third period for 3:17 without scoring. ... Sundqvist ended the Blues' goalless streak at 139:33. … St. Louis had not lost three straight in regulation since Dec. 4-10, 2019, and not lost three straight at home since Feb. 11-23, 2018.