McCown threw a touchdown pass in his debut for Cleveland and backup Johnny Manziel scrambled for a TD as the Browns, busting out new uniforms for the first time, built an early lead before losing 20-17 to the Redskins on Thursday night in their exhibition opener.
Signed to stabilize Cleveland's troublesome position, McCown connected with the wide-open Travis Benjamin on a 2-yard TD in the first quarter.
"He looked lonely, so I threw him the football," McCown said.
Griffin III went 4 of 8 passing for 36 yards during two possessions. Wide receiver Pierre Garcon dropped a long toss that would have been a TD.
Kirk Cousins rallied the Redskins, who trailed 14-3 in the second quarter. Cousins ran for a TD and went 12 of 14 for 154 yards.
Washington lost starting tight end Niles Paul to a broken ankle and running back Silas Reed sustained a knee injury.
"I'm sick about it," coach Jay Gruden said of Paul's season-ending injury. "He means a lot to this team."
McCown, who went just 1-10 as a starter last year with Tampa Bay, completed all five passes in his one series.
Washington's first-team offense didn't produce a touchdown in the preseason last year, foreshadowing Griffin's struggles in his third season.
Griffin has improved in training camp under new quarterbacks coach Matt Cavanaugh.
RGIII took a hit in the midsection on one play while rolling away from pressure, but still completed a 22-yard pass.
"You're going to get hit every now and then," Griffin said. "I thought we did a good job moving the ball. Get in, get out and that's all you can ask for."
Manziel made a smart play darting 12 yards for his TD. But the 2012 Heisman Trophy winner, trying to turn things around after a poor rookie season, stuck to his promise and skipped his signature "money" sign.
TIGHT END TROUBLES
Redskins: In addition to Paul's injury, TE Je'Ron Hall hurt one of his thighs. Washington was already missing TE Logan Paulsen, recovering from a torn toe ligament.
ON THE SIDELINE
Browns: Pro Bowlers Joe Thomas and Joe Haden both sat out. Thomas, who has never missed a snap in his NFL career, hurt his right leg during practice earlier in the week. Haden has been slowed by a hamstring issue the past week. Terrelle Pryor, attempting to switch from quarterback to wide receiver, didn't dress because of a lingering hamstring injury.
Redskins: RB Matt Jones ripped off a 23-yard run in the second quarter and finished with 38 yards on five carries. The third-round pick from Florida was checked for a concussion.
Browns: With Thomas out, first-round pick Cam Erving started at left tackle. Erving was called for a holding penalty that was declined.
Redskins: The secondary lost track of Benjamin on Cleveland's first TD. As McCown bought time, Benjamin crossed the end zone without a defender picking him up.
Browns: CB Justin Gilbert, a major disappointment as a rookie, got beat by Garcon and was lucky the Redskins' wide receiver couldn't handle Griffin's throw. Gilbert was beaten on other completions.
Redskins: Kai Forbath made field goals of 52 and 33 yards.
Pettine downplayed the Browns' interest in running back Ray Rice, suspended and released by Baltimore last year following a domestic violence incident.
"It is premature to talk about that," Pettine said. "We are comfortable with where our room is. I know a lot of people have connected the dots given his circumstances and ours, but it is too early to talk about it."