Dallas gave Walter Payton a throbbing headache and the Chicago Bears a 37-7 licking today in a one-sided National Football Conference playoff game that was settled 3 1/2 minutes into the third period.

When it was over, Payton claimed he couldn't remember a thing about the toughest football game of his life. Lucky for him.

The Cowboys, on the other hand, will recall a brilliant all-round effort that vaulted them into an NFC championship game Sunday in Texas Stadium.

The Cowboys moved a step closer to the Super Bowl with a running game that accounted for 233 of their 365 yards of total offense and a defense that limited Payton, the league's most dangerous running back, to 60 yards in 19 tortuous carries. The Cowboys had four interceptions and three fumble recoveries.

"I think at one point we had something like seven turnovers in eight series," said Chicago coach Jack Pardee. "You can't do that against the Dallas Cowboys. Had we not had any mistakes at all and played our best, we'd have still been in a heck of a fight."

Cowboy free safety Charlie Waters was one of many Cowboy heroes today, intercepting three Bob Avellini passes to tie an NEL playoff record.

Most of the players on both sides concurred that Waters' first interception of the day, late in the first half, ended most of the doubt about the thoroughly one-sided game.

The Cowboys, despite losing two fumbles on their first two possessions, nevertheless rolled to a 17-0 lead late in the second quarter. But the Bears were driving smartly toward a touchdown that might have made the game mere interesting.

On second and one from the 29-yard line. Avellini sent his tight end, Greg Latta, deep on a basic post pattern. Latta seemed wide open at the goal line as Avellini's looping pass headed his way.

But at the last possible moment, Waters came streaking in front of Latta for his interception. He hesitated a moment in the end zone, took a tenative step out on the playing field and ran 14 yards in all to kill the Bears' most serious threat of the day when the final outcome was still in doubt.

"I should have drilled the ball to Greg," Avellini said. "I had him there, and I didn't think Waters would be able to get back. I didn't think he had a chance to recover because he started away from the play."

But that was precisely what Waters wanted Avellini, the third-year Maryland man, to believe. "We were in a zone where Cliff Harris (the strong safety) and I split the field down the middle. Anything thrown down the middle we're supposed to go for.

"I wanted Avellini to think he (Latts) was open. As soon as he made his cut I knew Latta was the primary receiver. In that situation most quarterbacks will try and loft the ball in there when a guy's that open. If he had whipped it in there, I might have been in trouble. But then again, it would have been a tough catch to make. It worked out just like I hoped it would."

That was the case with everything the Cowboys attempted today. Roger Staubach had to throw only 13 passes, but three of those were mostly responsible for sending the Bears into hiberation for the long Chicago winter.

A 32-yard pass down the sideline to Tony Dorsett set up Doug Dennison's two-yard pop off left guard for the game's first touchdown with 1:06 left in the first period.

A 31-yard connection over the middle to Drew Pearson just over the out-stretched arm of Bear linebacker Tom Hicks set up Staubachs only touchdown toss of the day.

That came on the next play, when tight end Billy Joe DuPree went high in the air, with the sun in his eyes and two Bear defenders on his body, for a spectacular 28-yard scoring catch with 12 1/2 minutes left in the second period.

Avellini then helped kiss the game goodbye with two more critical turnovers - a pass interception by D.D. Lewis is to set up Tony Dorsett's 23-yard touchdown run on one of the sweetest little draw plays you'll ever see. Dorsett later scored from seven yards out, and had 85 yards in 17 carries for the day.

Avellini had the ball knocked loss by Terrible Tom Henderson on the next series as he tried to escape a safety blitz. The Cowboys turned that into a 31-yard Efren Herrera field goal, one of three chips shots he made.

With 11:24 left in the third period, the Cowboys had themselves a 27-0 lead, and many in the crowd of 62,920 began heading for the exits.

Payton probably wished he could have left, too.

Everywhere this muscular runner went, the Cowboys were close behind. "The flex defense is designed to plug every hole if you play it the right way," said middle linebacker Bob Bruenig. "Today, we played it the way it's drawn on th blackboard."

At the half, Chicago had only four first downs; Payton 18 yards rushing; and the Bears had not converted a single third down play.

Pardee talked about an overthrown pass to wide open Bo Rather early in the first period as one of several botched Bear opportunities that might have changed the final outcome. But he also admitted "their defense did one hell of a job on Payton."

"Right now, I don't even know what's happening." Payton said as reporters pressed around his locker. "My head is hurting. I don't want to seem rude or anything. I just got hit. It's the first time it's ever happened to me."

Payton was knocked groggy and fumbled early in the fourth quarter when hit by Harvey Martin and Randy White. Apparently his head never cleared, even though he played the entire fourth quarter.

In the Bear locker room, he kept holding his head, and walking around in a semidaze. Still, he had enough good sense to thank many of his linemen for helping him gain 1,852 yards in 1977.

"I'm appreciative of everything, Bod be with you," he told Latta.

"You're the best, Walter," Latta whispered in his ear.

But not today.