Goodman was banged up while trying to bring down Marion Barber in the third quarter.
Dawkins hurt his neck on a play late in the first quarter when he appeared to collide with teammate Robert Ayers as they tackled Barber. Dawkins stayed down on the turf for a few minutes before walking off the field on his own.
The Broncos won again, stunning the Bears 13-10 in overtime.
Information from The Associated Press contributed to this report.