Patrick Kane tallied one goal and one assist and Corey Crawford stopped 31 shots for the Blackhawks, who lost their second straight game and fell to 12-9-4 on the season.
"There was not much going on. We had the puck and then we'd give it away, and it's tough to get it back," said Kane. "We started buzzing a little bit in the third, and had some momentum which is good to see, but not much going on. We had 10 shots through two periods which is unacceptable."
The Stars penalty kill, which was 6-7 in the game, came up big early in the first period, killing off two Chicago power plays in the first seven minutes of the game although Chicago came close on the second one when Alex DeBrincat hit the crossbar.
The Stars grabbed a 1-0 lead at 14:46 of the first when Gemel Smith set up Janmark, who circled behind the Chicago net and scored on a wrap-around. But nine seconds later, DeBrincat scored off the rush to tie the game 1-1.
Chicago got a third power-play chance less than two minutes later, and Kane was called for hooking Faksa on a shorthanded breakaway which resulted in a penalty shot for the Dallas center. Faksa scored on the penalty shot, beating Crawford with a wrist shot to give Dallas a 2-1 lead at 17:20 of the first period.
"I think you could probably see the replay on the call on the penalty shot it looked like I just lifted his stick," Kane said. "But we had our fair share of chances on the power play, so we're not going to blame them, we should have done better on the power play, and it probably wouldn't have even went to that overtime."