After Chris Evert, the 23-year-old queen of American tennis, scored a U.S. Open quarterfinal victory yesterday over Tracy Austin, the 15-year-old princess-in-waiting, it was suggested they must look a bit like characters from "Alice Through the Looking Glass" to each other.

They have played three times in the past 15 months, and each time Austin has grown a little bigger, a little stronger, a little more formidable. She was 5 feet tall and weighed 90 pounds when they first met in the second round at Wimbledon in 1977. She is 5-3 and 110 now.

Evert has stayed about the same size - 5-5 1/2 and 125, give or take a couple of pounds - but from Austin's perspective she appears more of an equal in stature and skill, less an unapproachably imposing goddess.

At Wimbledon-77, on grass, Evert won, 6-1, 6-1.

At Hilton Head Island, S.C., last April, Evert won, 6-3, 6-1, on clay, a surface on which she has won 24 consecutive tournaments and 118 straight matches since the summer of 1973.

Yesterday, on a rubberized asphalt court that approximates the cement surfaces on which Austin learned, Evert won again, 7-5, 6-1. The first set was a cautious battle, the second a rapid execution.

The scores are getting closer, but Evert vs. Austin - The Present vs. The Future - is not quite a match yet.

"I wasn't really nervous, not compared to the first time at Wimbledon, because I knew what to expect," Exert said after the disappointingly dull match, which seldom roused the noontime early arrivals in a matinee crowd that eventually grew to 14,786 at the National Tennis Center in Flushing Meadow Park.

"I have enough confidence now to know that if I'm playing well, I'm still a notch ahead of Tracy. My ground strokes are just a little better than hers, so it's just a matter of getting myself psyched up and staying patient."

Evert, who next plays the winner of today's quarterfinal between Kathy May and Wendy (Rabbit) Turnbull, last year's runner-up, does not have any trouble getting psyched up for the U.S. Open.

She won the tournament the last three years, when it was played on clay at the West Side Tennis Club in nearby Forest Hills. She was the first winner of three consecutive titles since Maureen (Little Mo) Connolly in 1951-53, and she could become the first to win four straight since Helen Jacobs in 1932-35.

Evert has won 23 consecutive matches in U.S. opens, the longest streak since Jacobs won 23 through the 1936 final, which she lost to Alice Marble. Evert has won her past 16 matches in the Open, dating back to the 1975 final against Evonne Goolagong, without loss of a set.

Despite these facts, Evert properly is seeded No. 2 this year behind Martina Navratilova, who also advanced to the semifinals yesterday with an impressive 6-3, 6-2 victory over Virginia Ruzici or Romania, the French Open champ.

Navratilova's challenge to her superiority gives Evert added incentive here. Evert was the indisputable No. 1 woman player in the world for four years until Navratilova dominated the Virginia Slims Circuit in her absence last winter and beat her in the Wimbledon final. Evert is looking forward to another showdown.

"I think I'm playing better with each match," said Evert, who considered Austin an ideal quarterfinal opponent. She was confident she would win, but she knew she would be physically and mentally tested, and sharpened.

"This was a pressure match for me because Tracy is a tough competitor. Her mental attitude is so much better than most, and that's what posed a threat to me," said Evert, who admitted she has not watched Austin in the past four months but had read that she is growing stronger, hitting harder and playing more aggressively.

"Tracy doesn't crack, she doesn't choke, she just keeps hitting the ball. She doesn't look like she feels nervous out there. I think that's the big asset she has, the thing that makes her different from a lot of the other women players. So I think this was a good match for me to have."

For her part, Austin - who was Tracy in Wonderland when she reached the quarterfinals at Forest Hills last year at age 14 - the youngest player ever to compete in the U.S. Open - thought she had a chance to win yesterday.

She did not go into the match with the attitude of Caroline Stoll, Evert's third-round victim, who said she thought she had no chance and was out there merely for the experience.

"I watched that Little Mo thing last night. I thought that was interesting," said Austin, referring to a made-for-television movie about Maureen Connolly - her spectacular career, tragic career-ending riding accident and death from cancer at age 34.

Austin didn't finish her thoughts, but her smile left no doubt that she found inspiration in the story of Little Mo, the Californian with unerring ground strokes who won the U.S. Open at 16 and added three Wimbledon titles and two more U.S. crowns before her 20th birthday.

"I wanted to win and everything, but I still didn't know if I could yet," Austin said. "I felt I could trade ground strokes with her for awhile, and then she just came out stronger at the end of the first set. I got a little bit tired, and she started playing a lot better."

But Austin was not discouraged.

"At Wimbledon, it wasn't really a match. Chris was too good," she said. "I thought I played better at Hilton Head than at Wimbledon, and better here than at Hilton Head."

The future is creeping up on The Present, and knows it.

Austin might have done better if she had mixed up her game, following more first serves to the net, approaching on short balls, bringing Evert into the forecourt, instead of duelling from the backcourt - and a battle she cannot win yet.

Evert respects Austin's increasing flexibility. "She can play aggressively if she wants to or stay back and play conservatively if she wants to," Evert said. "She doesn't have a set game, like I did at 15."

She remembered that the first game Austin won against her at Wimbledon was accomplished by serving-and-volleying. Austin did not attack the net much yesterday, perhaps lulled into strategic complacency by the fact that Evert was uncharacteristically shaky from the backcourt in the first few games, taking some time to find her range.

But gradually Evert's ground strokes got steadier, deeper, more forcing. Austin found herself groping for defensive retrieves and squealing on lunges at balls she could not reach. She would not emulate Little Mo this year.

She got 85 percent of her first serves in, compared with 58 percent for Austin, and won numerous points with her service accuracy.