"We knew Todd can play football," Santana Moss, Redskins wide receiver, told reporters.
"He's been in this offense a lot longer than Jason [Campbell], so he knows pretty much everything, we just had to go out there and make plays for him."
The starting quarterbacks from both teams were injured early, with Chicago's Rex Grossman out in the first five minutes with a left knee injury and Washington's Jason Campbell suffering a dislocated left patella in the second quarter.
"The good news is they don't think it's ligaments," Redskins coach Joe Gibbs told reporters.
"They think it's a kneecap-type issue."
The Redskins, who lost 17-16 to Buffalo last week in their first game since Taylor's death, had only two days to prepare for the Bears, but they were ready.
Redskins defence stands up
Shawn Springs, who is also dealing with his diabetic father Ron, a former NFL rusher, having slipped into a coma last month after cardiac arrest, intercepted two passes within 30 seconds late in the first half.
Springs shut down two late Bears drives around a 21-yard touchdown pass from Collins to Todd Yoder that put Washington ahead 7-0 at half-time.
Collins, 36, had not thrown a touchdown pass since 2002 when he played for Kansas City.
Washington moved ahead 14-0 when Mike Sellers scored on a one-yard run after Clinton Portis ran 54 yards with a screen pass.
The Bears moved as close as 17-13 before Collins connected with Ladell Betts on a 16-yard touchdown pass with 2 minutes, 41 seconds to play for a 24-13 edge.
The Redskins ran for only 31 yards, their lowest total in a victory since 1974.