Three days after attending the funeral for slain teammate Sean Taylor, the Redskins (6-7) kept their playoff hopes alive in a game that saw both starting quarterbacks suffer knee injuries. Chicago's Rex Grossman left in the first period and Washington's Jason Campbell went out in the second.
Collins hit Todd Yoder with a 21-yard scoring throw with seven seconds left in the first half for the game's first points and all but clinched the victory with a 16-yard toss to Ladell Betts with 4:07 left in the fourth period.
Chicago got within eight when Robbie Gould kicked a 21-yard field goal with 30 seconds to go, but the Bears could not recover the onside kick. The defending NFC champions fell to 5-8, their playoff chances virtually gone.
Brian Griese replaced Grossman and threw for 295 yards and a touchdown. But he was intercepted twice.
The Redskins also got a one-yard scoring run from Mike Sellers in the third quarter and a 23-yard field goal from Shaun Suisham in the fourth.