LANDOVER, MD. -- With a national television audience focused on the progress of Cleveland rookie quarterback Johnny Manziel, the Washington Redskins overcame a slew of early mistakes and beat the Browns 24-23 Monday at FedEx Field.

Colt McCoy threw a 30-yard touchdown pass to wide receiver Nick Williams with 2:01 to play, breaking a 17-17 tie.

Cleveland tight end Emmanuel Ogbuehi outleaped a slew of players to haul in Connor Shaw's 45-yard Hail Mary pass on the final play, but Shaw's two-point pass fell incomplete.

The Redskins (2-0) outgained the Browns 185-80 with just over two minutes left in the first half but trailed 3-0 because quarterbacks Robert Griffin III and Kirk Cousins each had a poorly thrown ball intercepted and because running back Alfred Morris was thwarted on three consecutive carries from the 1-yard line.

Morris also failed to hold onto a pitch from Griffin on Washington's third play, turning the ball over. What's more, Griffin, whose fabulous rookie year of 2012 ended with a torn ACL, absorbed too many blows while trying to make things happen with his feet.

"It's something we have to continue to talk to (Robert) about, how important he is to this team and this franchise," Redskins rookie coach Jay Gruden said. "When he gets out of the pocket, he needs to protect himself. He needs to pick his shots and learn how to get down a little bit better."

Gruden was also somewhat frustrated by his team's mental mistakes.

"Part of my pregame speech was we have to eliminate penalties and protect the football, and we did neither," he said. "But overall, I'm fairly pleased. We're coming along at a good clip."

On the final drive of the first half, 35-year-old wide receiver Santana Moss rushed for 24 yards on third-and-19. Two plays later, Cousins found rookie receiver Ryan Grant for 15 yards, and two plays after that, running back Evan Royster powered for 24 on a short toss. Royster scored two plays later from the 2, giving Washington a 7-3 halftime lead.

Cousins opened the second half by completing all five of his passes for 48 yards, the last 14 yards coming on a toss to Grant in the right rear corner of the end zone for the touchdown that made it 14-3.

Griffin, who slumped in 2013 after his record-setting rookie campaign, connected on six of eight passes for 112 yards. However, he telegraphed a sideline throw for receiver DeSean Jackson -- making his Redskins debut -- that Browns cornerback Joe Haden picked off at the Cleveland 17 and returned 37 yards.

"I kind of floated it out there," Griffin said. "That's what happens when you play good corners like Joe Haden. If you make a mistake, they'll make you pay for it. ...

"We did a good job moving the ball ... but we can't hurt ourselves. We're getting too many penalties (11 for 100 yards). We still know there's a long way for us to go to get to where we want to be."

Cousins, who also played better as a rookie in 2012 than he did last year, overthrew receiver Aldrick Robinson on a deep ball that Browns safety Tashaun Gipson caught and returned 43 yards to set up Billy Cundiff's 29-yard field goal with 4:58 to go in the second quarter.

Cousins finished 12-for-21 for 145 yards with one touchdown and one interception.

Cleveland (0-2) was driving on its first series of the third quarter when Washington rookie cornerback Bashaud Breeland knocked the ball loose from ex-Redskins receiver Anthony Armstrong on fourth-and-1 at the Washington 26.

Manziel (7-for-16, 65 yards, one touchdown) finally got the Browns in the end zone with 13:33 remaining to close the gap to 14-10. The rookie quarterback, who is competing with holdover Brian Hoyer for the starting job, connected with running back Dion Lewis for an 8-yard touchdown.

Two plays later, safety Jim Leonhard picked off McCoy's first pass and returned it 19 yards for the go-ahead touchdown.

McCoy, who played for Cleveland from 2010-12, rebounded with a 43-yard completion to rookie receiver Rashad Ross on the next series, which ended with a 25-yard field goal by Kai Forbath that tied the score at 17-17 with 9:51 left.

Cundiff, who lost Washington's kicking job to Forbath in October 2012, was wide right on a 54-yard attempt with 5:24 remaining.

Hoyer completed two of six passes for 16 yards with no touchdowns and no interceptions.

"The first play was messed up," he said. "It kind of spiraled out of control. We were never able to get things going."

Speaking of the Browns' performance, Hoyer added, "It probably couldn't get any worse. It's disappointing, it's embarrassing."

NOTES: Browns WR Travis Benjamin (ribs) departed in the third quarter, while the Redskins lost CB Tracy Porter (hamstring), OLB Rob Jackson (sprained shoulder) and TE Niles Paul (hand). ... Washington won its eighth consecutive preseason game. ... DE Jason Hatcher (knee) was the only player expected to start for the Redskins this season who was sidelined Monday. ... DE Desmond Bryant (wrist) and CB Buster Skrine (thumb), both listed as starters, were among the 14 Browns unable to play. Skrine, who had surgery on the thumb Monday but could be back for the Sept. 7 opener at Pittsburgh, was one of six Cleveland defensive backs who were unavailable.