Chris Evert lost a set, the first she has dropped in the U.S. Open since 1975. Tracy Austin came within two tense points of losing to a semireformed volcano.

Jimmy Connors was twice down a break in the fourth set before he got his lava flowing. And Harold Solomon lost in five sets to Pat DuPre, who knew he had better get the match over with before he fell down with cramps.

It was that kind of day at the National Tennis Center. The weather was hot and muggy and the underdogs were biting like mosquitoes, which made for an uncomfortable afternoon of sweating and squirming for some of the favorites in America's premier tennis tournament.

Evert, Austin, Connors and Kerry Reid fought their way out of trouble. Solomon and Dianne Fromholtz did not. Only John McEnroe and Roscoe Tanner won their singles matches easily, and Tanner earned the dubious prize of meeting Bjorn Borg in a rematch of this year's Wimbledon final . . . in the Open quarterfinals.

Evert, a little sluggish and uncertain about how to play an aggressive opponent she had never faced before in singles, babied the ball for a set and then started walloping it to oust 20-year-old Sherry Acker, 4-6, 6-0, 6-2.

Austin, the 16-year-old teen queen who is seeded No. 3 behind Evert and Wimbledon champion Martina Navratilova, was down 5-6, 15-30 in a nervous third set against temperamental 19-year-old Pennsylvanian Kathy Jordan. But she held her serve and came from 3-4 behind in the tie breaker to win it, 7 points to 5, and the match, 4-6, 6-1, 7-6.

Connors, under fire and trailing 2-4 and 4-5 in the fourth set, psyched himself up with frenetic gestures after every winner and elevated his game to snuff out Brian Gottfried, 6-2, 1-6, 6-4, 7-5.

Reid, the No 8 seed, survived three furious sets against attacking 20-year-old Texan Anne Smith, 4-6, 7-5, 7-6. But fellow Australian Fromholtz, seeded No. 6, fell in a similarly tight battle to 19-year-old Sylvia Hanika of West Germany, 6-7, 6-4, 6-4.

And in the longest match of the wild afternoon session that attracted 16,546 paying customers-- most of whom must have wished they had three heads, so they could follow the activity on that many courts simultaneously-- DuPre won the last four games of a three-hour 12-minute battle of attrition to beat Soloman, 3-6, 6-3, 6-2, 4-6, 6-4.

The only players who won without unduly taxing their constitutions-- and those of the spectators-- were Tanner, who beat Tim Gullikson, 6-3, 6-4, 7-5, and McEnroe, who carved up Tom Gorman, 6-4, 6-2, 6-1, for the evening crowd of 10,204.

Tanner-- who served 16 aces, five of them on game points, in an impressive display of aggression on the asphalt-based hard court of Louis Armstrong Stadium-- thinks he has a reasonable chance of beating Borg, whom he led by two sets to one in this year's thrilling Wimbledon final. The fact that their match will be played under lights on Wednesday evening should be an advantage to Tanner, whose quick and deceptive left-handed serve is difficult to "read" even in broad daylight.

The rest of the quarterfinals men's pairings are Vitas Gerulaitis versus Johan Kriek, McEnroe against Eddie Dibbs, and DuPre versus Connors, a rematch of an exciting third-rounder here last year.

The women's quarters, like the men's, will be split between Wednesday and Thursday and pair Evert-Evonne Goolagong, Virginia Wade-Billie Jean King (oldies but goodies), Austin-Hanika (newies but goodies), and Reid-Navratilova.

The most agonizing of today's matches had to be the blood-and-sweat struggle between net-rusher DuPre and baseliner Solomon. DuPre wound up with cramps in both legs, Solomon with numbness in his racket hand. Both were spent and disheveled.

Solomon, who had not lost a set in the first three rounds, led by a set and 2-0. Then he was twice up a break in the fifth set, at 2-0 and 4-2, and had DuPre on the ropes again at 3-4, 15-40.

At that point, DuPre made a great swinging forehand volley winner at full stretch, though it tortured him to stretch. Solomon hit a forehand long, and DuPre served an ace for 4-4.

DuPre, whose talent blossomed as he reached the semifinals at Wimbledon this summer, was down 0-30 as he served for the match, but played four good points to seal the victory as he pounded his right thigh between points to stave off the cramps that occasionally made his legs "feel like a pretzel."

Even closer, though lacking the physical pathos, was Austin's victory over Jordan, a lanky, athletic, aggressive player given to tantrums, glares and throwing rackets.

Jordan, victor over Austin for the first time at an indoor tournament in Philadelphia this spring, does not have as violent a temper as she once did, but she still queries calls, chastises herself, and smolders incessantly. "I think the linesmen don't believe her after a while," Austin remarked afterward, "because she questions every call."

Austin's face betrayed little anxiety, but she played a terribly nervous match, particularly in the third set, making an uncharacteristic number of unforced erros. "She shouldn't outsteady me in rallies," Austin said. "I couldn't understand it."

Jordan is an agile volleyer who covers the net superbly, but she is vulnerable from the back court and has a strictly defensive backhand. She had six break points for a 4-2 lead in the third set, but couldn't capitalize on any-- even though Austin curiously kept going for the lines on a day when she couldn't find them.

The next four games all went against service, Austin hitting short and ragged, Jordan winning points at the net but not getting there often enough.

Jordan finally held for 6-5. Austin was two points from defeat when she sprayed a backhand cross-court wide for 15-30.

But she played the next three points safely to get into the tie breaker.

Austin won four of the last five points of the tie breaker from 3-4 down. On her second match point-- after Jordan had saved one with an uncharacteristically attacking backhand winner-- Austin finally hit the sort of shot expected of her: a ripping backhand cross-court return that forced a diving backhand volley error from Jordan.

At practically the same time, Evert was losing the first set to the surprised and surprising Acker, a chunky but quick-reflexed serve-volleyer from Kalamazoo, Mich.

Evert, 24, has won 29 consecutive matches to win her four straight Opens and reach the quarters of what would be a record fifth in a row. The last time she lost a set was in 1975 final, to Goolagong.

"I was a little tentative in the first set, and I was a little discouraged at that point. I thought, 'Well, this is ridiculous, I'm not playing my game. Just play your game and hit out on the ball,'" Evert related.

"Sherry played very well the first set. I had no idea what to expect from her. She deserved to win that set (whick Acker did on her seventh set point), and I knew I had to come up with some answers.

"I couldn't find a weakness in her game at first because she was so quick at the net and she anticipated my passing shots. But in the second set I hustled a little more, to get to the drop shots and short balls. I really had to lift my game to another level."

Connors also responded just when Gottfried seemed to have him at the ledge, producing his best shots to break back twice in the fourth set. "The last three games, he played awfully doggone well," said Gottfried. "That's when it mattered. He raised his game, and I didn't."

Gottfried had one break point in the 11th game, but Connors held and then punished Gottfried's second serves again-- Gottfried was in peril whenever he missed first serves and had to stay back-- and broke for the match.

By this time, Connors was strutting, arching his back, throwing up his arms in almost manic gestures of superiority at every winner. "I didn't play great most of the match, but I definitely played better at the end," Connors said. "My whole game elevated."