Chicago (5-1) employed a stingy defense, forcing three Detroit turnovers in the red zone.
Matt Forte rushed for 96 yards on 22 carries and Marshall finished with six grabs for 81 yards as the Bears won their fourth straight.
The Lions (2-4) finally scored with 30 seconds remaining when Matthew Stafford connected with Ryan Broyles on a 12-yard TD pass, but they couldn't recover the ensuing onside kickoff.
Stafford ended by going 28-for-46 through the air for 261 yards in the loss.
Celebrity Families of 2014 [PHOTOS]