The surprise team in the NFL this season, the playoff-bound Bears (11-3) improved to 8-0 in games decided by seven points or less.
"That shows the character of our team," Bears coach Dick Jauron said. "The kind of football we play, we play together and we play to our strengths on both sides of the ball. By not trying to be who we're not, when it comes down to crunch time, we have what it takes to win."
Chicago faced a 13-10 deficit when Paul Edinger lined up for a 44-yard field goal. But Maynard, the holder, rolled right and found a wide-open Urlacher at the 15-yard line. The 244-pound linebacker, who caught six touchdown passes in college, raced to the end zone for his first touchdown reception in the NFL.
"We practiced that play this week. I think we put it in just for this game," said Urlacher, who also led the Bears with nine tackles. "I dropped a couple of passes in Friday's practice, but Brad made a great pass today. The main thing was to catch the ball and not worry about scoring."
"We have a couple of people that are assigned to look for that kind of play. I haven't spoken to those players to see what happened," Redskins coach Marty Schottenheimer said.
"Generally, you anticipate something like that happening. But even if you're prepared for it, if you're not looking for the right things, you can come up short. You have to give the Bears credit. It was a great play."
Edinger kicked his second field goal of the game, a 37-yarder with 4:23 to play, to extend the lead to 20-13.
Washington (6-8) did not have a first down for the first 12 minutes of the fourth quarter, but finally got untracked and threatened to tie it.
Tony Banks completed four passes for 48 yards during a desperation drive, including a nine-yarder to Rod Gardner that moved the Redskins to the Bears' three with 1:45 remaining. But Stephen Davis was stopped for no gain on second down and Banks threw a pair of incompletions.
"We have to make more plays in the red zone," Banks said. "We're not getting the job done, either running or passing. We put ourselves into too many third and longs, either with penalties or sacks."
Maynard stepped out of the end zone for a safety with 20 seconds left and Eric Metcalf fumbled the ensuing free kick, ending Washington's playoff hopes.
"I'm disappointed. I'm disappointed for our fans, I'm disappointed for our players because they have taken every opportunity to do the very best they can," Schottenheimer said. "I am not accustomed to not being in the playoffs, so obviously it's very disappointing."
Chicago hounded Banks all afternoon, sacking him tix times.
"We made the plays when we had to," Urlacher said. "They're a good offensive team, they run the ball pretty well. We made plays when we had to and that's what the game comes down to."
The Bears' Autry Denson fumbled the opening kickoff, but Banks returned the favor on the third play from scrimmage, with linebacker Rosevelt Colvin recovering at the Chicago 34-yard line. After rookie Anthony Thomas carried three times for 18 yards before Edinger kicked a 39-yard field goal to open the scoring.
Michael Bates returned the ensuing kickoff 30 yards and the Redskins drove 57 yards to the go-ahead touchdown. Stephen Davis did much of the work, gaining 30 yards on six carries and giving Washington a 7-3 lead with a three-yard run.
But Davis managed just 27 yards on 16 attempts the rest of the way against the NFC's top-ranked rushing defense.
The Bears regained the lead on the first play of the second quarter, when Leon Johnson raced 32 yards for a touchdown -- his longest carry of the season.
The Redskins took the ensuing kickoff and moved 49 yards in 12 plays. Four plays after Banks threw an 11-yard pass to Michael Westbrook on fourth and six, Brett Conway tied it with a 34-yard field goal.
Conway kicked a 26-yarder on Washington's second possession of the second half, capping a 72-yard drive on which Banks completed third-down passes to tight end Zeron Flemister and Gardner. But the Redskins came up empty on three plays from the eight-yard line.
"We came up short again. It's a play here and a play there," Schottenheimer said. "The bottom line is, we have to try to find a way to get the ball in the end zone when we have it inside the 20. You can't just kick field goals in this league and expect to win against good football teams."
The Bears rallied to end a six-game losing streak against the Redskins, defeating them for the first time since a 34-14 triumph in 1988.