Myers made it 2-0 at 9:01. Connor scored his first of the game at 13:38 to make it 3-0.
"We didn't have a shot for like the first what, 15, 16 minutes? Maybe even more," Blackhawks forward Patrick Kane said. "Pretty embarrassing start."
Connor scored his second of the game at 1:44 of the second period on the power play to make it 4-0.
"There's nothing really more we can say about the starts," Kane said. "Spot them four goals, it's tough to come back in this league."
Strome scored at 2:04 before Kahun made it 4-2 at 7:09.
Connor nearly had a hat trick, but Ward made a sprawling glove save at 17:23.
Chicago scored its third unanswered goal when DeBrincat made it 4-3 at 6:08 of the third period.
Perreault pushed the lead to 5-3 on the power play at 11:36. Connor missed an empty net with 1:03 remaining, but Tanev scored at 19:55 for the 6-3 final score.
"Nothing really changed," Connor said. "Just stuck with the plan. We knew what we had to do. We've been in that situation quite a bit this year and ended up getting the win."