The Bears (1-3) got a win after starting 0-3 for the second time in as many seasons under Fox. They also stopped a six-game home losing streak as well as a six-game slide against Detroit (1-3), though things got tight near the end.
Fox has been noncommittal when asked if Cutler will start when he is ready to return, and he wasn't about to tip his hand after this one. Chicago visits Indianapolis next week.
"I'd like to enjoy this for at least a few hours," Fox said.
Hoyer shrugged off a similar question, saying, "It's my role to do whatever's asked of me. Today, I'm going to enjoy the victory. Whatever they say to me tomorrow, then that's what I'll prepare to do. I think that's being a professional about it."
The Lions dropped their third straight, with Stafford struggling to find open receivers and a short-handed run game once again unable to get going.
Marvin Jones Jr. had 74 yards receiving after setting a career high with 205 yards against Green Bay the previous week.
"We were just not sharp at all," coach Jim Caldwell said. "There was no rhythm to it. That's my fault."
Copyright 2016 by The Associated Press