Jason Dickinson, Sam Lafferty and Taylor Raddysh scored for the Blackhawks (4-3-1), who have lost two in a row.
"We got away from our skating game a little bit, and it doesn't take much for that team to make you pay," Lafferty said. "So yeah, disappointing, but some good things to build on for tomorrow (against the Minnesota Wild)."
Arvid Soderblom made 41 saves in his season debut.
"He played great. He really deserved better tonight, and I thought he looked really calm in there, made some really big saves on chances that were primaries," Chicago coach Luke Richardson said. "That's something we want to clean up as a team, especially in front of a young goaltender, but he showed a lot of poise out there. It was nice to see."
Thompson narrowed it to 3-2 at 11:55 of the third, sweeping in the rebound of Okposo's initial shot in front. He then tied it 3-3 at 16:47 when he batted the puck out of the air near the right post following a wraparound attempt by Skinner.
"I think it was just a matter of time," said Thompson, who had eight shots on goal for the second straight game. "If you're getting chances, I think that's all you can really ask for. If you're not getting chances, that's when you've kind of got to be looking yourself in the mirror to see what's going on. If you're getting chances, I think they're bound to go in. Previous game, maybe facing a hot goalie and unlucky bounces here or there, so it was nice to get a couple tonight."