McCown had a hand in five touchdowns as the Bears romped to a 45-28 victory over the Cowboys, throwing four scoring passes and running for one of his own.
The 34-year-old has filled in for Cutler seven times already this season, including the last four games in a row, throwing for 1,809 yards, 13 touchdowns and just one interception in that time.
However, McCown is under no illusion that he is merely a temporary fix until Cutler is able to return from his ankle injury, and he has outlined his desire to continue performing well whenever he was called upon.
"The team knows who the starting quarterback is, and like I said before, I know my job as the backup. I want to play efficient football, winning football and keep us in contention while the starter is not healthy," McCown told reporters.
"As long as Jay is healthy and ready to go I don't think there's any question. I just want to do my part so we'll see what happens moving forward."
The win sees the Bears move level with the Detroit Lions at the top of the NFC North with just three games of the regular season remaining.