Doomsday descended on the Washington Redskins yesterday in a farcical football game that was singularly embarrassing and cast a shadow on their hopes of winning the NFC East Division title.

"Washington Slept Here," read a Texas Stadium banner, and the white-hot Dallas Cowboys took advantage of the Redskins' Somnambulant state for a 37-10 rout, the most lopsided Washington loss since 1970.

The cowboys became 9-4 and dropped the Redskins to 8-5. Even if they tie with the same regular-season record, Dallas will win the division title. The Cowboys can be no worse than 5-3 in the division. The Redskins, who are 4-4, and would lose under the tie-breaking procedure.

Any combination of Dallas victories and Washington losses adding up to two would give the Cowboys the crown. The same formula applies to the Cowboys and third-place Philadelphia Eagles.

"It's humiliating," said Redskin defensive end Coy Bacon. "I've never been beat this bad the whole time I've played football. I just can't agree with this at all. We were flat. You say it. We had no killer instinct. We did nothing out there.

I tell you something else. All this other bull has to stop. Jack Pardee is not getting enough respect. It makes me sick to see it. He's the man, he's the coach. Respect is our biggest problem.

"People aren't listening to him. You can't question the man's decision, and that's what's been going on around here. We're not close enough. We're falling apart, and I hate to see it.The man is trying as hard as he can. It's got to change.

"Nah, I'm not gonna say anything. All the speeches have to go. It's time to play some ball now. Talk is cheap. We win the next three, we might go to the playoffs. We have the talent, but we have to get hungry again."

The Cowboys, of course, were ravenous yesterday. They gained 507 yards, made mincemeat out of Joe Theismann's battered body, built up a 20-0 lead by halftime and were never threatened in posting their ninth victory in 13 starts.

Still, Pardee insisted when the debacle was over that his team still has a decent shot at the playoffs as a wild-card entry despite its fifth loss in seven games, a defeat that leaves it 8-5 for the season.

"We're got three weeks left, and the playoffs are a good possibility," he said. "We have a lot to be thankful for, even though we lost today. We've got the nucleus of a good team here Everyone is trying. We're not thinking about changing around; we're thinking about how to win.

"We have a chance as long as everyone is trying and everyone is. Oh, there may be an exception of two. I don't see it (dissension), no more than on any other team. I thought our team hung together pretty well under adverse conditions. I don't think we'd have any dissension if you people (members of the media) would quit asking about it."

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Many Redskins were asking what train had just run over them. The Dallas Express began chugging when the Redskins put themselves in a hole on the opening kickoff with a personal foul by Ike Forte. They finished with 100 yards in penalties and only 202 yards offense.

The cowboys could do no wrong in front of a howling Texas Stadium crowd of 64,905. Scott Laidlaw, making his first start replacing injured Robert Newhouse, gained more than 100 yards by halftime and finished with 122 and two short touchdown runs.

Quarterback Roger Staubach was deadly accurate when it counted most - heaving a 53-yard touchdown pass to Drew Pearson 2 1/2 minutes into the second period for a 20-0 Dallas lead.

Before Dallas Coach Tom Landry mercifully pulled Staubach and ordered reserve Danny White to kill the clock with 9:49 left, Staubach had completed nine of 19 passes for 218 yards. He also scrambled frequently to pick up first downs. He gained 27 yards in seven runs.

The game became such a rout that early in the third quarter Cowboy linebacker Tom Henderson, on the sideline, was shouting at the Redskins, "It's Pearl Harbor for you guys . . . Tora! Tora! Tora!"

It was the biggest margin of defeat for the Redskins since Dec. 6, 1970, when the Cowboys won, 34-0, in Dallas. The last time a team scored 37 or more points against the Redskins was a 45-21 romp by the Cowboys in Washington Nov. 22, 1970.

"We came out ready to go," Staubach said. "I'm surprised we won like we did. I expected it to be a tight game. I was surprised at the score."

Landry said, "It was going to be hard to stop us today. We were emotional and we jelled. There is no question about it."

The Dallas coach said the Cowboys were "ready to play this game more than we have been ready all year.

"Last year in the stretch, we had a lot of games like this," he added, "but we haven't had as strong an outing as this game this year.

"It's still not over. The race can change overnight. All I know is that we won our last three games decisively."

The Redskins once again self-destructed early. Fullback John Riggins accepted a good share of the blame because of a blunder he described as significant as any play all day - his fumble on the Redskins' 14-yard line midway through the period.

After the Cowboys had opened a 6-0 lead on field goals of 33 and 21 yards by Rafael Septien, Riggins was running hard on his first carry of the day. He was smacked with an equal amount of force by line-backer Bob Bruenig and defensive tackle Randy White. The ball popped forward, was scooped up by cornerback Benny Barnes and returned 14 yards to the Washington Six.

Four plays later, on third and one, Laidlaw bulled into the end zone behind guard Burton Lawless and, with the extra points the Cowboys were up, 13-0.

The Redskins, meanwhile, were mostly going backward. On their first 13 plays from scrimmage, they had two penalties, one sack, one fumble, four incomplete passes and no first downs.

The Cowboys stretched their advantage to 20-0 early in the second period on their first play after a Mike Bragg punt put them at their 47.

Pearson, the Cowboy receiver who caught four passes for 116 yards, got a two-step advantage on Redskin cornerback Joe Lavender down the left sideline, caught Staubach's pass in full stride and hot-footed into the zone.

The Redskins were unable to get past midfield in the first half and were fortunate to go to the locker room at intermission trailing by only 20.

After 30 minutes, they had managed only four first downs (two via penalty), had gained one yard passing, 44 yards rushing and had been forced to punt a half dozen times. The Cowboys, meanwhile, had scored on four of their first five passessions.

Theismann had the wind knocked out of him late in the second quarter and was replaced by Billy Kilmer. But Pardee went back to Theismann for the entire second half in the face of a foursome Cowboy pass rush that managed only three sacks but harassed Theismann all afternoon.

Theismann finished with 10 completions in 24 passes for 150 yards. Most came in the second half, when he connected with tight end Jean Fugett for a 16-yard touchdown pass with 2:17 left in the game.It was for too little, far too late.

The closest the Redskins got after intermission came on Mark Moseley's 48-yard goal less than three minutes into the third quarter, cutting the lead to 20-30. But Staubach drove his team right back to set up Septien's 44-yard field goal for a 23-3 lead with 7:09 left in the third period.

And two series later, the Cowboys drove from their 36 to Laidlaw's second touchdown, a two-yard run, on three plays. The first was a 12-yard gain by Tony Dorsett that became a 27-yard pickup when the Redskins were penalized for a face-mask violation.

Staubach threw over the middle to Drew Pearson for 35 yards more and Laidlaw blew off left tackle for the score that left no doubt as to the final outcome, giving Dallas a 30-3 lead.

Larry Brinson, a seldom-used reserve whose rushing total for the season was a minus-two yards, finished the Dallas scoring orgy with a 39-yard run down the right sideline, even as the Cowboys were merely content to hand off the ball and not humiliate the Redskins any further.

That touchdown provided a 37-3 lead, and even Landry could hardly supress a smile of sheer delight.