CHICAGO -- Washington Redskins quarterback Kirk Cousins knows that standing under center is akin to buckling in for a roller-coaster ride.

So after Cousins led Washington to a 24-21 win over the Chicago Bears on Sunday, he avoided making any major pronouncements about what the victory represented for himself and his team.

"I've had games where people want to run me out of town," Cousins said with a smile. "The next week, we win, and I'm the greatest thing since sliced bread. I just keep trying to grow and build on each experience I have, whether it's positive or negative, and trust that if I do that good things will happen."

After a long drought, good things finally happened to the Redskins on the road. Washington (6-7) snapped a nine-game road losing streak and earned its first win away from home since Oct. 27, 2014.

Cousins completed 24 of 31 passes for 300 yards and a touchdown and rushed for another touchdown. Redskins tight end Jordan Reed hauled in nine passes for 120 yards and a touchdown to lead all receivers.

"We have everything that we want still in front of us," Washington coach Jay Gruden said. "It keeps us alive. It keeps our heart beating, heart pumping. Guys should be excited to come back to work Monday."

In the opposite locker room, Chicago (5-8) struggled to find answers after another narrow defeat. The Bears' past five losses have come by single digits.

Chicago coach John Fox said a slow start ultimately cost his team.

"All I know is you have to work harder and get better," Fox said. "It's not lack of effort, it's not lack of want to. We are in positions to have an opportunity to win games and we just come up short."

The score was even at 21 when kicker Dustin Hopkins drilled a 47-yard field goal to put Washington ahead 24-21 with 14:07 remaining in the fourth quarter.

Chicago's comeback attempt fizzled when kicker Robbie Gould missed a 50-yard field goal attempt with 1:40 to go. Gould had enough distance on the kick but missed wide right.

"It comes down to one play," said Gould, who also missed a potential game-winning field goal one week ago against San Francisco. "My teammates rely on me. And the last two weeks, I just haven't got it done."

The Redskins built upon a 14-7 halftime lead with a touchdown on their first possession of the second half. Cousins hit Reed on a crossing route for a 5-yard score that made it 21-7.

Reed surpassed 100 receiving yards for the first time this season and the third time in his career.

"He's a problem for a lot of people," Gruden said. "In man to man, he's very good against a linebacker, safety or nickel. In zone, he's very good at reading zones and sitting down. He's a friendly target, quite frankly. He has been good for us."

Chicago rallied with a pair of touchdowns to even the score at 21 late in the third quarter. Cutler connected with tight end Zach Miller for a 9-yard touchdown pass with 3:42 remaining in the third quarter. Less than three minutes later, running back Matt Forte scored on a 7-yard run.

Washington opened the scoring when running back Alfred Morris pushed across the goal line for a 1-yard touchdown run with 6:30 remaining in the first quarter. Morris' first touchdown of the season capped a marathon 15-play, 80-yard scoring drive that chewed 8:30 off the clock.

Cousins increased the Redskins' lead to 14-0 on a 3-yard run with 14:19 to go in the second quarter.

The Bears pulled within 14-7 when Cutler found wide receiver Alshon Jeffery for a 20-yard touchdown pass in the final minute of the first half.

Cutler finished 19 for 31 for 315 yards, two touchdowns and no interceptions.

Cousins said he and his teammates earned the win on the road.

"It's not an easy thing to do," Cousins said. "It felt like it took the whole team. It took special teams plays, defensive plays, offensive plays. It took a lot of different guys making plays and contributing to find a way."

NOTES: Bears WR Eddie Royal returned to the starting lineup after missing the previous five games because of a knee injury. ... Redskins TE Derek Carrier limped off the field and did not return after injuring his right knee in the first quarter. ... Bears LB Willie Young registered a sack for the fourth consecutive game. ... Redskins RB Pierre Thomas made his team debut two days after signing a free-agent deal. Thomas replaced RB Chris Thompson, who missed the game because of a shoulder injury. ... Bears S Antrel Rolle (knee) missed his fourth consecutive game and his sixth game of the season.