The Washington Redskins backup QB Kirk Cousins leads the team to their fifth straight win in a row to put them on top of the NFC East igniting playoffs hopes in the Washington region. (The Washington Post)

The Washington Redskins protected their future by sitting down prized rookie quarterback Robert Griffin III on Sunday. That did nothing to harm their present, as rookie backup Kirk Cousins threw a pair of touchdown passes and led the Redskins to a 38-21 victory over the Cleveland Browns.

The Redskins won their fifth straight game, improving their record to 8-6 and moving into a first-place tie with the New York Giants and Dallas Cowboys atop the NFC East. Washington holds a tiebreaker advantage over the Giants based on a superior division record, as well as over the Cowboys by virtue of their 38-31 win in Dallas on Thanksgiving, though the Redskins and Cowboys will play again at FedEx Field in the regular season finale on Dec. 30.

“The main thing is we control our own destiny,” Redskins Coach Mike Shanahan said. “We know that. So any time you can control your own destiny with two weeks to go, it’s all you can ask your football team to do. We’ve worked extremely hard to get to this point. The job’s not done.”

With Griffin on the Redskins’ inactive list because of a sprained lateral collateral ligament in his right knee and watching the game from the sideline, Cousins completed 26 of 37 passes for 329 yards in his first NFL start. He helped the Browns to an early touchdown with an interception but rebounded to throw a pair of touchdown passes to wide receiver Leonard Hankerson.

“This isn’t my first rodeo,” said Cousins, a fourth-round draft pick in April from Michigan State. “I did play a lot of football in the Big Ten and I had games like that where you start slow and you’ve got to have character. You’ve got to find it within yourself to dig deep and keep pushing. . . . We just found our rhythm. We got a good tempo going and we got our rhythm. It made all the difference.”

Tailback Alfred Morris ran for a pair of touchdowns for the Redskins, who scored 21 consecutive points to turn a 14-10 halftime deficit into a 31-14 fourth-quarter advantage. The Redskins scored 28 second-half points. Reserve running back Evan Royster also had a rushing touchdown.

Rookie tailback Trent Richardson had two touchdown runs for the Browns (5-9), who had a three-game winning streak ended. Quarterback Brandon Weeden threw for 244 yards and a touchdown for Cleveland. But Weeden also threw a pair of interceptions and generally was outplayed by fellow rookie Cousins.

Weeden’s 69-yard touchdown pass to rookie wide receiver Travis Benjamin pulled the Browns to within 31-21 with about 10 minutes remaining. But the Redskins replied with Morris’s second touchdown, an eight-yard run.

“It says a lot about the talent we have here and the character guys we have here,” Morris said of winning without Griffin.

Cousins had made two relief appearances this season, one of them a week before this start when Griffin hurt his knee late in the fourth quarter of the Redskins’ overtime triumph over the Baltimore Ravens.

Cousins and the rest of the offense had a sluggish start as the Redskins failed to earn a first down on their first four possessions. The second possession ended with Cousins throwing a pass into heavy traffic around on a third-and-10 play. Cousins’s pass was tipped by Browns cornerback Sheldon Brown to safety T.J. Ward, who made the interception and raced 37 yards before Cousins tackled him at the 6-yard line. Richardson scored from there.

Cousins and the Redskins settled down, however, grabbing a 10-7 lead on Cousins’s 54-yard touchdown pass to Hankerson and place kicker Kai Forbath’s 44-yard field goal. Weeden managed only 88 first-half passing yards, but 30 of them came on a second-quarter completion to wide receiver Greg Little to set up Richardson’s second touchdown.

That gave the Browns a 14-10 halftime lead, but the Redskins moved in front with two quick touchdowns in the third quarter. Weeden threw a pass directly to Redskins linebacker Rob Jackson for an interception, putting the Redskins in business at the Cleveland 15-yard line. That led to Morris’s three-yard touchdown run. The Browns punted and the Redskins drove to their second Cousins-to-Hankerson touchdown. On a third-down play from the Cleveland 2, Cousins passed to the wide-open Hankerson on the right side.

Weeden’s problems continued when he threw another pass to a Redskins linebacker, this time London Fletcher, for a second interception of the third quarter. Royster’s four-yard touchdown run early in the fourth quarter upped the lead to 31-14.

“It’s a lot of guys, a lot of great coaching, a lot of depth, a lot of players that are second string and third string that are stepping up for us and making plays when we really need it,” wideout Pierre Garcon said.