"Broadway" Vitas Gerulaitis has long been known as a character in international tennis, a lover of expensive cars, flashy designer clothes, stylish women and life in the fast lane. He has been cast as the Joe Namath of the short-pants jet set, able to disco til dawn and still win most of his matches without breaking a sweat.

But in winning the Italian Open a week ago in a torturous five-set classic over Argentinian Guillermo Vilas, Gerulaitis demonstrated a different sort of character, a gut-fighting spirit that few thought he possessed.

It was a match in which Gerulaitis easily could have reconciled giving up. He led, 5-3, in each of the first three sets but lost the first and third in tie breakers. After 3 1/2 hours, he found himself two sets to one-down.

It was 90 degrees on the dusty-red campo centrale (center court) at Rome's Foro Italico. Vilas, who had lost only eight games in two previous matches against Gerulaitis, both on clay, was fit and strong and very much in his element. Few people believed that Gerulaitis would make a battle of it in the fourth set, especially after he let a 3-1 lead slip to a 3-4 deficit.

But he hung in, refused to admit fatigue, and won the second-most important clay-court title of Europe for the second time in three years, 6-7, 7-6, 6-7, 6-4, 6-2.The match lasted 4 hours 53 minutes, excluding the 17-minute intermission between the third and fourth sets and was thought to be the longest final ever in a major international championship.

"I didn't give up in that match, that's for sure," Gerulaitis said today, thinking back a week after vanquishing Ivan Lendl, the 19-year-old Czech who beat Arthur Ashe on Friday. The 6-2, 6-1, 6-3 win puts Gerulaitis in the quarterfinals of the French Open, the world's premier clay-court championship.

"I know that maybe last year or the year before, I might just have said, "This is a waste of time. I've served for three sets, lost two of them, I've been out here 3 1/2 hours, I might just as well bag this.'

"Even if I hadn't really stopped trying to win, I know I would have mentally let down. But I've realized that the biggest difference between me and the only guys I haven't been able to beat, (Bjorn) Borg and (Jimmy) Connors, may be most mental. You've just got to keep sticking in there all the time, never letting up.

"The mental aspect is the toughest part of tennis, and I never really appreciated that until the last year or so. But it's true. If your mind is tense, your body is going to be tense. It's not the other way around. If you've got the talent, your brain is the final say, because the body does what the brain tells it."

Gerulaitis, 24, was relaxing now on the terrace of the players' dining room at sold-out Stade Roland Garros, gulping fresh orange juice squeezed specially for him by an admiring and amply-tipped barman. His long blond hair was dripping from his postmatch shower, but he had put on fresh tennis clothes and track suit, preparing to go out for an hour's practice with his coach, Australian Fred Stolle.

Gerulaitis has been working overtime the past month, four to six hours a day when he is not in a tournament, an hour or two after his tournament matches, getting himself into the best shape of his life for a full-scale assault on Wimbledon starting three weeks from Monday.

His long sessions of conditioning and practice with Stolle are dedicated to Borg, Connors and the wunderkind, John McEnroe, the three players ahead of him in the computerized world rankings of the Association of Tennis Professionals. Gerulaitis wants desperately to join them in what he has dubbed "the Two-Mile High Club."

"Connors said a funny thing the other day," he began again, picking up his theme about the mental side of tennis after some good-natured badinage with the waiter who brought him his beloved O. J.

"We were talking about people thinking while they're playing. He said, "I don't have that problem because I never think.' He kind of said it in jest, but there may be a little bit of truth there, because he goes out and plays instinctively. He just belts the hell out of the ball. And Borg, too.

"I mean, they play intelligently . They move guys around, play short and long, do all the right things tactically. But they play more by instinct, especially when they're down.

"It was the same with Rod Laver when he was the best. When those guys are down, it's like putting a tiger to the wall. They're going to fight to kill and get out of there.

"I've always played a little bit more conservatively, defensively, to get out of tight positions. Against maybe 95 percent of the players that works, but it doesn't work against the top five, because they're not going to miss."

Gerulaitis readily admits that after surging past most of his contemporaries, winning the Italian Open in 1977, the Australian Open and World Championship of Tennis titles in 1978, and taking up residence at a lofty level just below Borg, Connors and Vilas, he grew a little complacent.

Having earned $811,088 in prize money in his first five years as a professional plus perhaps three times as much again in endorsement and exhibition revenues, he decided to enjoy his Rolls-Royces, his palatial home in Kings Point, Long Island, his nights out with the glitterati in the garden spots of the world.

But the sudden ascendance of McEnroe last winter jolted him back to attention. For a brief time, Gerulaitis fell to No. 5 on the computer. (He since has passed Vilas and is currently behind only Borg, Connors and McEnroe). He decided it was time to get back to work.

"It wasn't McEnroe personally, but I saw there were going to be guys like that who, if you don't keep on top of your game, are going to sneak in there ahead of you," Gerulaitis said today.

"So it was good that he came along, actually. It put me back on my toes. It put Borg and Connors back on their toes, too. If it wasn't for McEnroe I might still be sitting in a bar somewhere, enjoying myself but not getting any closer to the guys ahead of me."

Until the Italian, Gerulaitis had won one tournament this year, a minor event in Little Rock. He seldom lost before the semifinals of a tournament, but he wasn't fighting like a tiger against the wall in the tough matches. He took a leaf from Connors' book and went to work.

"I decided to work my tail off for six weeks to get ready for Wimbledon, then take most of the summer off and do the same thing a couple of weeks before the U. S. Open.I think that's a lot better way than playing yourself silly all year," he said.

"All the work I've been doing the last few weeks has been geared toward Wimbledon. If I won that one title, that would put me in the club. That would be enough satisfaction for me. But it's nice to win these others, too - especially the Italian, because it was Vilas and such a tough match."

Gerulaitis hired Stolle - champion of France in 1965, Forest Hills in 1966, and three-time runner-up at Wimbledon - to coach him individually after playing for him on the New York Apples of World Team Tennis.

"There was nobody else left. All the other coaches were taken," a joshing Gerulaitis deadpanned today, when asked why he had chosen Stolle.

Later he answered the question seriously, pointing out that Stolle is a disciple of the old Australian school of hard conditioning, discipline and aggressive play, things he needs to be reminded of.

Stolle is not business manager, babysitter, valet of surrogate father to his pupil, as some modern coaches are to top players. But he is a friendly taskmaster.

"Fred was too great a player, I respect him too much to have him be like a nursemaid, wiping my nose and fixing my food and all that stuff," Gerulaitis said.

"We're working on a lot of things, technically and tactically: serve, volley, approach shots, drop shots. He's fixing up my footwork a little bit on the ground strokes, where I got sloppy. We talk about opponents and strategy, and he works me physically.

"But I'm still the horse. I've got to win the race. The trainer knows how to prepare the horse - what he's got to eat, how many furlongs he'a got to run in practice, all of that - but the horse still has to run. . . .

"During matches, there's very little Fred can tell me that I don't already know. I may look at him once in awhile and he might nod or say, 'Let's go.' but that's the same as when I look at my sister (Ruta, 23, who plays Chris Evert Monday in the women's singles quarterfinals here).

"She says, 'Come on, stupid, let's go!'" CAPTION: Picture, Vitas Gerulaitis returns shot to Ivan Lendl. AP