Through a quarter of the season, the Washington Redskins maintained good health at all their key positions, and Mike Shanahan’s players had managed to keep their errors to a minimum — both factors in their early success and first-place standing in the NFC East.

Sunday, as they looked to protect their division lead against the visiting Philadelphia Eagles , all that good fortune came to an end in a 20-13 defeat before a crowd of 80,447 at FedEx Field.

The Redskins suffered three first-half injuries on offense — losing starting guard Kory Lichtensteiger, probably for the season, with torn ligaments in his knee; tight end Chris Cooley to a fractured index finger in his left hand that will require surgery and tackle Trent Williams to a sprained ankle. They saw quarterback Rex Grossman throw four interceptions before he was benched.

John Beck took over, playing both of the Redskins’ fourth-quarter possessions, but couldn’t complete the comeback, and Washington — whose defense held in the second half after giving up 20 first-half points — dropped to 3-2 on the season.

Meanwhile, the New York Giants won their game against the Buffalo Bills and improved to 4-2 to take over first place in the NFC East. The Eagles, who had lost four straight games, won their second straight game at FedEx Field, and may have saved their season. No team in NFL history has ever overcome a 1-5 start to win its division.

“There were a lot of things that were a problem today,” said Grossman, who completed only nine of his 22 passes and posted an anemic quarterback rating of 23.7. “First of all, we didn’t take advantage of the opportunities that were given us as an offense. And I didn’t execute.”

Grossman, who started the final three games of Washington’s season in 2010 and beat out Beck for the starting job during training camp, endured his worst outing as a Redskin. His struggles started early.

On Washington’s fourth offensive snap of the game — a third-and-16 play from the Philadelphia 38, the same play on which Lichtensteiger’s season likely ended — Grossman threw an interception to Philadelphia safety Kurt Coleman while trying to hit tight end Fred Davis 34 yards downfield.

The Eagles turned that interception into seven points, stringing together an 11-play drive that quarterback Michael Vick capped with a seven-yard toss to tight end Brent Celek.

The second quarter saw Philadelphia score another touchdown and two field goals, as Washington’s offense continued to struggle. Grossman threw another interception and at halftime, the Redskins had only a field goal to show for the game, and trailed 20-3. Cooley left the game midway through the quarter, and Williams limped off two series later.

In two quarters, the Eagles outgained the Redskins 250-75, earned three times as many first downs (16-5) and dominated their hosts in time of possession, 21 minutes 38 seconds to 8:22. (For the game, the Eagles outgained Washington 422-287, had 22 first downs to the Redskins’ 17, and held the ball for 38:08 while Washington did for 21:52.)

Shanahan stuck with Grossman when the third quarter began. But after a defensive stand on which the Redskins briefly knocked Vick out of the game and DeAngelo Hall intercepted the ball at the Philadelphia 18, Grossman threw another pick to Coleman, who returned it to the 29.

Grossman got one more chance, but on third and nine from the Washington 39, Grossman’s 22nd pass attempt of the game went to a wide-open Coleman. With that, offensive coordinator Kyle Shanahan, who was standing on the sideline, threw up his hands, hurriedly walked up to Beck, barked “You’re in” at the quarterback and slapped him on the back.

“Obviously, I would have liked to have finished what I started,” said Grossman, who has thrown nine interceptions this season. “There are a lot of times . . . when things aren’t going well and then all of a sudden, things go into place and everything gets better, you start to click and all of a sudden get into a rhythm. I wasn’t able to do that, and they thought that was the best answer to replace me for that specific kind of spark.”

After the game, Shanahan said: “Number one, we needed a spark. John’s been practicing very well the last couple of weeks. And with four turnovers there, we thought it was time to give John an opportunity to show what he can do.”

But by that point, the damage was done.

Washington’s defense continued to keep the Eagles off the scoreboard. But the Redskins had to punt on Beck’s first series on the field. Beck came back to lead the team on a 10-play, 80-yard scoring drive that ended with him plunging in from two yards on a quarterback draw with 2:44 to play.

The Redskins missed a chance to score at least a field goal on Beck’s first series, when they committed their ninth penalty of the game. They reached the Philadelphia 33, but were stopped on third and 17. Graham Gano, who had nailed a 50-yard field goal earlier in the game, came on to attempt a 51-yarder on fourth down, but Washington instead was called for delay of game. No one was in injured tackle Williams’s spot, and Will Montgomery ran on late to fill the void.

Rather than go for a 56-yarder, Shanahan — whose team racked up a season-high 75 yards in penalties — sent on the punt unit.

Washington’s defense recorded two second-half interceptions (one by safety Oshiomogho Atogwe, the other by Hall) but couldn’t get the ball back for the offense on its final stand. The defense gave up a one-yard run to Vick on a third-and-one quarterback keeper with two minutes left, and the Eagles were able to run out the clock after that with three straight kneel-downs.

Beck finished the game with 117 yards passing on 8 of 15 attempts and added 14 yards rushing on two carries.

Although Beck did provide a brief spark in limited action, Shanahan declined to say who would start next week against the Carolina Panthers. Beck hadn’t played in a regular season game since 2007 and completed 30 of 48 passes for 356 yards, a touchdown and two interceptions during the preseason.

“I would never announce that right after a game,” Shanahan said. “I would announce that later on in the week. We’ll make a decision after looking at the film.”

In addition to their budding quarterback conflict, the Redskins must address their losses on the offensive line. When Lichtensteiger went down, starting center Montgomery slid over to left guard, and Erik Cook — a 2010 seventh-round pick, who spent the bulk of his rookie season on the practice squad — took over at center. Washington doesn’t have another guard or center on the roster.

At tight end, fourth-year pro Davis has served as Washington’s go-to guy with Cooley hobbled by a knee injury. He recorded six catches for 95 yards Sunday, and Logan Paulsen served as Washington’s second tight end after Cooley left the game.