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.
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.
"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."
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.
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.
Jeffery added to it with that neat catch after Dallas was forced to punt.
Copyright 2013 by The Associated Press