The news was encouraging on both counts. Sampras, the defending champion, recovered to overhaul Magnus Larsson, of Sweden, 4-6, 6-7, 7-5, 6-4, 6-4, and Gullikson, who has heart problems, appears to be on the mend. He is expected to be discharged within the next two days in order to return to the United States.
Had Larsson, the No 15 seed, held his game together for a few crucial points in the third set, Sampras and Gullikson would be travelling home together. As it is, Sampras campaigns on into a quarter-final tomorrow against his compatriot, Jim Courier.
The Americans have a score to settle. Sampras, having relieved Courier of the No 1 position, terminated his two-year reign at Flinders Park with a straight-sets win in the semi-finals 12 months ago. Courier responded by ending Sampras's prospects of winning the French Open with a quarter-final victory on the Paris clay in June.
"It's ironic," Sampras said. "Magnus is not a good guy in my draw." Larsson has become associated with problems for Sampras, though the only time he has lost to the Swede was in the final of the Grand Slam Cup in Munich last month.
On that occasion, Gullikson was taken to hospital on the opening day of the tournament with the second of two minor strokes. The first related to his collapse during the Stockholm Open in October, two days before Sampras played Larsson in the quarter-finals.
Sampras spoke with Gullikson on the eve of yesterday's match - "just a couple of details about what I can try and do" - and said he was thinking about his coach during the contest, "trying to pull it through for him."
It was the American's 100th Grand Slam singles contest, but for a two and a half sets Larsson made him appear a novice rather than a world champion, complementing a powerful serve with punishing groundstrokes, particularly on the forehand.
"Basically, I was getting outplayed," Sampras acknowledged. "I didn't play my best tennis, but he was playing too good for me. If he was going to maintain that level for a little bit more, he could have pulled it out."
Larsson found himself tantalisingly close to victory with Sampras serving at 4-5, 15-30. At that stage, Sampras said, "you just have to rely on instinct and reaction". So he made a potent delivery and watched the return go over the baseline for 30-30.
A backhand volley then took Sampras to game point, but he missed a forehand and beckoned Larsson back to deuce. A smash gave Sampras the advantage again, and Larsson's forehand let him down when he attempted to fire a winner down the line.
"I think he just got a little tight when it came to the crunch time in the third set," Sampras said, "and then he got down on himself in the fourth and the fifth. I was lucky to win, basically. Two points from being out of the tournament is a little bit too close for comfort."
Courier, the No 9 seed, continued an impressive advance with a fourth consecutive straight-sets win, defeating Karel Novacek, 6-2, 6-3, 6-2. The unseeded Czech who outsmarted Michael Stich in the previous round by adopting an attacking game, was unable to counter the Floridian's groundstrokes.
Pete played a nearly flawless match against me [here] last year," Courier said. "If he plays another match like that, I'm going to have my work cut out for me. I think I played into his hands in that match and gave him what he needed to play his best. I just hit the ball where he likes it to be hit. I won't do that again knowingly."
Sampras will not be without support, though his girlfriend, Delaina, has her left arm in plaster after breaking her wrist in a road accident on the way to the airport to travel here.
There is a third American quarter-finalist in the top half of the draw, Michael Chang, the fifth seed, defeating the unseeded Olivier Delaitre, of France, 6-3, 6-2, 6-4.
The Stars and Stripes would have been guaranteed one finalist had the unseeded David Wheaton secured victory in a five-set duel with the No 13 seed, Andrei Medvedev. The Ukrainian triumphed after almost three and a half hours, 3-6, 6-3, 6-4, 6-7, 10-8, and now plays Chang.
Medvedev's girlfriend, Anke Huber, watched the final set, which provided some consolation for the 10th seed's 6-2, 6-4 defeat by Mary Pierce. Huber's elimination means that Germany will not have a quarter-finalist of either sex in the singles event of a Grand Slam championship for the first time since Wimbledon in 1984.
As projected, Pierce, the No 4 seed, will play Natasha Zvereva, the No 8 seed, who beat Kyoko Nagatsuka, 3-6, 6-3, 6-1. Natasha is the competitor from Belarus who used to be presented as Natalia but has requested the informal version.
"I'm always looking for a change," she explained. "I change my hair, change my name. Natalia is a passport name, and I think's it's way too official. Natasha is kind of nice and soft and mellow."
Conchita Martinez, the No 2 seed, stumbles on. The Wimbledon champion led Irina Spirlea by a set and 4-1, and then made sufficient errors to encourage the unseeded but dangerous young Romanian to make a a match of it. Martinez asserted herself in the third set to win 6-2, 6-7, 6-2.
The Spaniard now faces a repeat of her Wimbledon quarter-final against Lindsay Davenport, the sixth seed from the United States.
Davenport defeated Brenda Shultz, of the Netherlands, 6-2, 3-6, 6-2 - not so much a score, perhaps, as a question concerning their respective heights. Davenport, at 6ft 21/2in, edged that contest, too.
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