The Philadelphia Eagles won the National Football Conference's Eastern Division title today -- it was their first championship since 1960 -- but their success raised serious questions about the playoff qualifying system because they backed into the title.

The Dallas Cowboys, humiliated by the Los Angeles Rams, 38-14, last Monday night, bounced back today to beat the Eagles, 35-27. It was the Eagles' third loss in four games.

The Cowboys had to beat the Eagles by at least 25 points to win the title under the NFL's tie-breaking system. The Cowboys led by 25 early in the fourth quarter, but their pass defense collapsed. The Eagles scored 17 unanswered points. Cowboy Tony Dorsett's fumble of a lateral.

The Cowboys had already clinched a wild card spot and will meet the Rams here in postseason competition Sunday.

The Eagles and Cowboys finished 12-4 and the tie was broken on the basis of best net points in the division.

"I can say we lost the battle but won the war," said Coach Dick Vermeil of the Eagles. "Last year, I felt we tied Dallas for the division title and they won it. Today, we tied them again, but we won it.

"It was very frustrating there in the first half with all the bad field position and the horrible officiating. Yes, horrible officiating. Maybe I'll be fined, but I think it's time for coaches in this league to speak out. iOn Jerry Robinson's long (71 yards) interception return, they called holding on one of our guys (nullifying the interception) and then couldn't even tell me who it was that held."

Vermeil raised some eyebrows with his remarks about Tony Franklin missing three of five field goal attempts. Fraklin was wide from 43, 27 and 25 yards, but hit from 29 and 19.

"As for Franklin not hitting those field goals," Vermeil said, "I can't do anything for him. It's very demoralizing, not only to him, but to the whole team. It's all mental and Tony has to get his act together.

"I hope he grew up today. If he didn't he won't be kicking in this league anymore."

The game ended Eagle Harold Carmichael's record pass-catching streak of 127 games. In a 1972 game against the Washington Redskins, Carmichael caught a pass, and he had caught at least one in every game since. Today the streak ended when Dennis Thurman knocked him out of the game when Carmichael was trying to catch a sideline pass.

"We played a super ball game," Tom Landry, coach of the Cowboys, said after the victory, in which Danny White threw four touchdown passes and plunged for another score. "I thought we were okay until we got the 25-point difference, then we lost our concentration. The momentum swung then."

Quarterback Ron Jaworski of the Eagles threw only one touchdown pass, a 30-yarder to wide receiver Rodney Parker. But it began the 17-point assault in the final period which cut the 35-10 deficit.

The crusher to the Cowboys' dwindling title hopes came when White was blitzed at his 20-yard line. He lateraled to Dorsett, who fumbled. Linebacker Robinson recovered at the Dallas six-yard line, and on first down, Montgomery ran for a touchdown with 1:56 to go. Only then did the Cowboys, the highest-scoring team in the NFL, seem ready to concede.