At the end of the fourth set, after the defending champion had fought back from two sets down for the second consecutive match, a spectator shouted: "Do it for your coach, Pete!"
This proved to be too much for the 23-year-old Sampras, who wept almost uncontrollably during the change-over after winning the opening game of the final set, and could barely serve through his tears in the third game.
Gullikson was on his way back to the United States after being discharged from hospital. Last Friday he was taken ill for the third time in three months, having already suffered two minor strokes before accompanying Sampras to Australia.
A crowd of 15,000 fell silent as Sampras walked around, desperately trying to control himself. Courier, seeing his friend and rival in distress, called out: "You doing OK, Pete? We can do this again tomorrow, you know." Sampras's girlfriend, Delaina Mulcahy, tried to console him by shouting, "Just hang in there, honey!"
In spite of his anguish, Sampras conceded only two points on his serve in the final set as he advanced, 6-7, 6-7, 6-3, 6-4, 6-3, to a semi-final meeting tomorrow with Michael Chang, another American compatriot.
Judging by the state Sampras was in when the Courier match ended at 1am, after almost four hours, it will be a major achievement if he is able to raise his game again.
Prior to the interviews, Paul McNamee, the tournament director, read a statement confirming that Sampras's discomfort on the court was due to being upset by Gullikson's illness, and requesting questions relating only to the match. Sampras then entered the room, but had to leave immediately when the tears began to well again.
After a few moments, he returned and explained, haltingly, the reason why the trainer had paid frequent visits to the court to treat his right foot. "I just had a little cut on my toe, and I just had to get it taped up," he said.
Had he also, like his opponent, experienced cramping? "No, I wasn't cramping. I was pretty much flat out, pretty tired.''
When asked to repeat the comment that he had made to Sampras at the finish, Courier remarked: "I said, `I know you're dead, because I'm dead'."
The dramatic climax was only one feature of a contest which stands comparison with some of the epics of recent memory: Chang against Ivan Lendl at the 1989 French Open and Petr Korda on successive nights against Sampras and Michael Stich at the 1993 Grand Slam Cup in Munich.
Sampras and Courier produced a match of quality as well as excitement, tighter than their four-set 1993 Wimbledon final and enhanced by the rallying which is possible on the rubberised concrete surface at Flinders Park.
Courier, the ninth seed, demonstrated how much his desire to play had improved since Sampras dispatched him in straights sets in the semi-finals a year ago. For most of the match he was hitting the ball as hard and accurately and moving as quickly as when he won the title consecutively in 1992 and 1993.
"I've been in a few good matches," Courier said, "but I realised going into the second set something special was happening out there. We were both not missing very much, and all the points were being fought for."
Sampras, who came back from two sets down to defeat Magnus Larsson, the No 15 seed, on Sunday, dropped the opening sets to Courier without losing his serve.
He recovered after losing the tie-breaks, 7-4 and 7-3 respectively, but found himself 2-4 down in the fourth set. Courier was broken for 4-4, after double-faulting on a game point, and wildly hit a smash wide on Sampras' second set point.
"I don't feel bad about this match at all," he said. "I know I played well and did what I needed to do all through the match, and I just physically gave out. The other guy was physically giving out, too. We both could have collapsed any minute. But he was the one standing, so he's the one who gets to play the next round."
Chang, the fifth seed, defeated the No 13, Andrei Medvedev, 7-6, 7-5, 6-3, though before the opening set was concluded it seemed case of who would be forced to retire first.
The American twice called the trainer to treat muscular problems during change-overs, and Medvedev sprained his left wrist when falling heavily during the tie-break. Fortunately, both players recovered.
Chang dismissed his physical difficulty as "just a little bit of tightness - we'll leave it at that, because Jim and Pete read papars." Medvedev said his wrist was numb for the remainder of the match, "but it didn't bother me playing".
The Ukrainian, having recovered his composure, created the first set point, at 6-5 in the shoot-out. Chang snatched it away, passing him down the line, and then gained the advantage, 9-7.
In the second set, as in the first, Chang moved 3-0 ahead, only for Medvedev to whittle the lead away and take the initiative, 3-5. The American responded by winning the next nine games.
"There were a lot of crazy things happening out there," Chang said. Leading 5-0 in the third set, he was broken twice before cracking Medvedev's serve for the match.
In the women's semi-finals, Conchita Martinez, the Wimbledon champion, will play Mary Pierce for the first time. The Spaniard, seeded No 2, won a laborious quarter-final against the tall American, Lindsay Davenport, 6-3, 4-6, 6-3. The match ended on a double-fault, one of 50 unforced errors the sixth seed donated towards Martinez's 87 points. Pierce, the No 4 seed, defeated the No 8 seed, Natasha Zvereva, of Belarus, 6-1, 6-4.
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