The loss left Dallas (7-6) a game behind Philadelphia in the NFC East and owner Jerry Jones calling for more aggressive play-calling on defense.
The bone-chilling conditions didn't stop McCown from throwing for 348 yards or keep the Bears from running away with a lopsided victory.
It was one they desperately needed after consecutive losses, and although Detroit holds the head-to-head sweep, the Bears are back in the thick of the playoff race.
"All we could do is try to beat the Dallas Cowboys," coach Marc Trestman said. "We kept it as simple as that. We didn't get into all the hypotheticals and all the things that go into winning or losing a game."
Alshon Jeffery's leaping catch between two defenders in the corner of the end zone in the closing seconds of the second quarter gave the Bears a 24-14 lead, and they continued to pour it on in the second half after a gut-wrenching overtime loss at Minnesota last week.
Here are five things we learned on a frigid night at Soldier Field:
STILL NO. 2: No matter how well McCown plays, the Bears insist he's still the back up to Jay Cutler.
Even after the veteran became the first Bears quarterback to throw for 300 or more yards, that message came through.
Cutler will get his job back once he's ready to return from a high left ankle sprain. McCown will get a nice pat on the back and maybe a contract for next season.
"We'll see where Jay is this week," he said. "He'll have to be released by the doctors and when Jay is ready to play, he'll be playing."
NO DEFENSE: Jerry Jones isn't happy, either. The Cowboys boast the league's worst defense, and after watching Chicago rack up 490 yards, their owner is calling for some changes.
"Basically, we will have to make some adjustments in what we are doing defensively," Jones said. "What that usually means is taking more risks on defense. But if you're going to have the kind of match like we had tonight or certainly in New Orleans you have to take some risks. We have to double up and I'm sure that will be part of the plan on defense; more risks."
DOMINANT DUO: No matter who's throwing them the ball, Brandon Marshall and Alshon Jeffery continue to wreak havoc.
Marshall caught six passes for 100 yards, giving him 1,090 on the season. Jeffery is now up to 1,193. He had 84 yards receiving after breaking his own team record the previous week with 249.
STOPPING THE RUN: The Bears came in ranked last against the run, and they continued to struggle in that area. They held Tony Romo to 104 yards passing but couldn't do much against the run. DeMarco Murray ran for 146 yards, and the Cowboys finished with 198 rushing on just 28 carries.
A ROMO FADE?: Romo's regular-season record as a starter in December and January is now 12-17. But Jones insisted he's not concerned by that.
"I really don't think I ever made a decision regarding Tony in any way that involved a thought about his December record," he said. "It's not an issue. We need to win a game. We need to win next week. The December thing is not a big factor."
AP NFL website: www.pro32.ap.org