It was a case of murder in the afternoon, but there was no need to examine Bon Lutz's body after the final of the $100,000 Volvo Tennis Classic yesterday. The 5,000 witnesses knew the corpse had Brian Gottfried's foot-prints all over it.

As so often happens in tennis tournaments, the sellout crowd at the final saw a match that did not live up to the standards of excitement set in earlier contests.

Saturday's semifinals had been marvelously competitive: Gottfried beating Raul Ramirez and Lutz outsting Tom Gorman, both in three excruciating sets. Gottfried trampled Lutz, 6-1, 6-2, yesterday in just 50 minutes at George Washington Universith's Smith Center.

Gottfried, 25, the Floridian who is ranked No. 5 in the U.S., has gotten his act together impressively in the last six months.

He has consolidated his abundant all-court skills with a positive mental attitude and compiled a season record of 26-3. He has climbed to No. 7 in the computerized world rankings of the Association of Tennis Professionals, based on tournament results over the last year.

Gottfried has won three tournaments in the 1977 Colgate Grand Prix series. His victory here, worth $20,000, follows triumphs in the Towson (Md.) International Airlines Tennis Games at palm Springs last month.

"In the last three months, Brian has definitely been among the top three players in the world," said Lutz, 29, who never had a chance to get his powerful strokes grooved, and couldn't find his usually sure touch on the lob and volley.

"Tennis players go in streaks. I played Arthur Ashe in two finals at this time last year, when he was winning five out of six tournaments. Maybe next week Brian will play like a bum . . . Right now, he's at the uppermost peak of his game."

Lutz got some solace in the doubles final. He teamed with longtime partner Stan Smith, with whom he has been ranked No. 1 in the U.S. five times, for a 6-3, 7-5 victory over Gottfried and Ramirez, the reigning Wimbledon champs and No. 1 team in the world.

At the presentation ceremony for the singles match, Lutz had apologized to the crowd for the brevity of that final. "Hopefully Stan and I will make a bit of a run of it in the doubles and give you your money's worth," he said to loud applause.

That they did, and Lutz got his money's worth as well. He split $6,000 with Smith in addition to the $10,000 be collected as singles runner-up. Gottfried and Ramirez divided $3,6000 as their share of the doubles purse.

Still, the singles final was fraught with frustration for the muscular Lutz. He was runner-up in the $100,000 Ocean City International last month, but has not won a significant tournament since April, 1975.

"He really didn't let me into the match at any stage. Even my best serves he was pounding back," said the Californian, U.S. pro champion in 1972 before injuries necessitating surgery on both knees put valleys into a career of lofty promise.

"I missed some easy shots. I hit some good ones, and he made better ones off them. Maybe if I had hit my volleys with a little more, authority he couldn't have made so any passing shots. But he didn't miss much and I just never felt in it."

By the middle of the first set, Lutz was bedraggled. He perspires heavily, and his shirt was soaked through, his lank hair matted into a porcupine coiffure.

Gottfried, returning superbly off both wings, broke Lutz four of the seven times he served. Meanwhile, Gottfried had only two break points against him, in the third game in the last game of the match.

Both times he brushed them aside, the first with a forehand volley down the line that wrong-footed Lutz so badly that he fell in a heap on the court, the second with a good serve that forced a return error.

Gottfried jumped on Lutz early and kept him down.

In the sixth game, for example, Lutz was serving at 1-4, 0-15. Nearly caught at the net by one of Gottfried's well-disguised lobs, he spun, leaped and angled a backhand overhead cross-court that should have been a clean winner.

But Gottfried is quicker than he looks and he looks very speedy. He ran down the ball and cracked a sharply-angled backhand cross-court that clipped the sideline. Now it was 0-30, and he went on to break for 5-1.

"That isn't a high percentage shot, but if I make it I really feel good," Gottfried said with a smile. "It's also bound to discourage him."

Gottfried approached extremely well on Lutz backhand, and was nearly flawless at the net. Lutz prefers the same territory, but he was skewered repeatedly by Gottfried's passing shots and lobs.

Lutz was so demoralized by his own ragged play and Gottfried's unrelenting onslaught that he was reduced to muttering exasperated asides as the momentum built: "That's just stinko" . . . "I don't understand it" . . . "I'm glad everything's working."

Gottfried, playing on a heady crest of confidence, traces his change in attitude back to a match he lost to Bjorn Borg in the fourth round of the U.S. Open last September after leading 2-0 in sets and 2-0 in the third.

"I remember it prefectly," he said."It was 30-30 in the third game, and I served a double-fault. He won the next point and then raised his game and wore me down.

"After the match I wasn't really upset because I knew I had played well. But I realized it was ridiculous: I came that close to winning a big match and never felt that I should or could win. I was playing to make it close. Obviously that was wrong.

"I made an effort to change that kind of thinking and be more positive. Then things started failing into place."

The next week, Gottfried and Ramirez won a $100,000 doubkles only tournament, then Gottfried ran off 11 straight singles matches, winning the Pacific Soothwest Open at Los Angeles over Ashe, reaching the final at San Francisco the following week.

He has made a substantial technical improvement in his second serve, but said that "probably at least 60 per cent of my improvement is mental.

"If those wins had been scattered, I might have said, 'I had a couple of good weeks, but nothing solid,'" Gottfried explained. "As it was, those wins did something for me at a time when my mind was ready to let it happen."