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.
McCown, making his fourth straight start with Jay Cutler sidelined by a high left ankle sprain, completed 27 of 36 passes.
Brandon Marshall caught six passes for 100 yards, and Jeffery added 84 yards receiving after breaking his own team record the previous week with 249.
Matt Forte chipped in with 102 yards rushing and 73 receiving, and the Bears racked up 490 yards in all.
"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."
Tony Romo threw for three touchdowns but completed just 11 of 20 passes for 104 yards for Dallas. DeMarco Murray ran for 146 yards against the league's worst run defense, but the Cowboys were overmatched after winning two straight.
They also lost linebacker Sean Lee to another injury this time a neck issue after making a tackle in the third quarter. He missed the previous two games with a hamstring problem.
"Certainly, it was a disappointing loss and the loss stings," coach Jason Garrett said. "The worst thing we can do is have a hangover after this loss."
The game-time temperature was 8 degrees with the wind chill at minus 9, but the freezing conditions did nothing to slow either team in the early going. Garrett said both teams handled it well.
Murray burned Chicago for 52 yards on six carries on the game's opening possession to set up a 2-yard scoring pass from Romo to Dez Bryant, but the Bears scored just about every time they got the ball.
After Bryant's TD, McCown tied it with a 4-yard pass to Earl Bennett and put Chicago ahead 14-7 early in the second quarter with a 7-yard scramble, leaping at the goal line and getting spun in midair.
Storylines Bears 45, Cowboys 28
R Chicago's Josh McCown throws a career-high four touchdown passes as the Bears beat Dallas.
• The Bears retire Hall of Famer Mike Ditka's No. 89 during a halftime ceremony.
• With the loss, Dallas (7-6) falls a game behind Philadelphia (8-5) in the NFC East.