Now, on the eve of the French Open, these exploits must seem very distant in the memory. For 1995, by his own high standards, has been a disappointment, underscored by the sadness of seeing his coach of two years' standing, Tim Gullikson, forced out of the game by a brain tumour, for which he began a six-month course of chemotherapy in March.
In Gullikson's absence, Sampras has turned for guidance to Paul Annacone, a doubles specialist who at 32, with most of his career behind him, is in a similar category to Brad Gilbert, Andre Agassi's coach: the near- contemporary who has been around a bit and whose insights are perhaps greater than their achievements. And, importantly, coaches in the Annacone mould tend to operate in a friendlier, lower-key, more egalitarian mode than would apply with many in their position.
Like Sampras, there is something of the all-American boy about Annacone, with his 1950s, college-boy, traditional air which, in the case of the two-times Wimbledon champion, is often taken for boringness. Annacone had coached only juniors before, but he has a friendship with Sampras that goes back 10 years, and from stepping into the breach in Australia he has now, in effect, taken over until Gullikson can return, and that almost certainly will not be before next year. He and Gullikson talk on the phone every week. "It's been a very easy transition," Annacone says. "We have pretty much the same philosophy."
Annacone thus finds himself central to Sampras's efforts to recover a lot of lost ground - more than is suggested merely by the surrender of his No 1 position to Agassi, whose defeat of Sampras in the final of the Australian Open in January marked the start of this period of relative decline.
Since then, the sure, soft tread of the man who has been described as the perfect tennis player has turned into a stutter. In eight tournaments since Australia, not including an appearance in the Davis Cup, Sampras has won only one, at Indian Wells in March. With the start of the clay- court season, he really lost his way: beaten in his opening matches in Barcelona, where his conqueror was a German, Oliver Gross, ranked 84th in the world, and in Monte Carlo, where he had to retire with an ankle injury while playing Paul Haarhuis of Holland.
When Sampras returned to action in Hamburg, he reached the semi-finals before being knocked out by Andrei Medvedev. But in the Italian Open in Rome two weeks ago, it was back to square one - beaten in the first round again, by the Frenchman Fabrice Santoro. It has been, at best, a patchy season on the clay which Sampras was making a special effort to master in the build-up to Roland Garros and the one Grand Slam title that he, like Agassi, has never won.
Annacone plays down Sampras's loss of form, ascribing it mainly to "a bit of bad luck and a topsy-turvy schedule". But he agrees that Gullikson's illness and the changes it has occasioned - Sampras has just acquired a new personal trainer, Todd Snyder - have unsettled him. "These things always take a bit of acclimatisation." And he concedes that some of the criticisms Gullikson made of Sampras after his defeat by Jim Courier in the quarter-finals of the French last year - essentially that he did not vary his game enough - still apply.
"The thing with Pete is that he's incredibly versatile," Annacone says. "He's got all the tools of the trade. But sometimes he has difficulty using all those tools, and then he becomes just like any of the other guys on the tour. When you're used to winning as much as Pete is you get into patterns, and it's not so easy to change them when you have to. You get comfortable doing things in a certain way.
"Obviously with a player like Pete you're not talking about big adjustments. Nothing too technical or fancy. The goal is to make his strengths even better, and the thing I like about Pete is, even with all he's achieved, he still wants to work at that."
That's what he was doing in Paris last week where he practised with Michael Chang and, according to Annacone, was hitting the ball well and feeling confident. He will need to be at his best from the outset, having been given a tough first-round draw against Gilbert Schaller, of Austria, a useful clay-courter who beat Sergi Bruguera, winner of the past two French Opens, earlier this year. And if he reaches the quarter-finals, it is Bruguera who is scheduled to stand in his way. The greatest players love a challenge, but Sampras's desire for this one will need to be very keen indeed.Reuse content