Roger Federer does not often surprise himself, but he gave the impression after playing the sort of tennis of which only he or an angel is capable that an 18th major really is not beyond him this weekend, even at 35.

After defeating the German left‑hander Mischa Zverev 6-1, 7-5, 6-2 on day nine of the Australian Open, Federer is the oldest player to reach a slam semi‑final since Jimmy Connors, then 39, did so at the US Open in 1991. The oldest semi-finalist here before Federer was the 34-year-old Arthur Ashe, in 1978.

If he were to go all the way and win on Sunday, he would be the oldest champion to win three majors after turning 30 since Ken Rosewall, who completed his hat-trick here 45 years ago.

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On Thursday Federer plays his relatively youthful compatriot Stan Wawrinka, 31, for a place in the final and a shot at securing his fifth Australian title, one behind Novak Djokovic – and five more than Andy Murray, who might take a week or two to get over losing against the world No50 Zverev in the fourth round, just two days after the equally unexpected exit of Djokovic.

That has been Federer’s astonishing achievement here: returning from six months off the Tour while recovering from knee surgery to outlast players five and six years younger than him, in-form, elite performers who were expected to crowd him out of the picture yet again. He has not won a slam since Wimbledon five years ago; after five performances of varying brilliance, he is one of the last four standing.

Federer’s tennis against Zverev on Tuesday night in Melbourne was from another era. Against a relentless serve-volleyer, he passed and lobbed and smashed and chipped his way to a victory as commanding as any when in his pomp. He hit 65 winners and just 13 unforced errors in a 90-minute demolition. That is nearing perfection.

His single-handed backhand was in its old groove and his court presence grew by the point. Zverev, who did not play that badly, was outclassed from the first set – which lasted a mere 19 minutes – to the final imperious forehand winner that left him rooted to the baseline.

Facebook Twitter Pinterest Stan Wawrinka, right, beat Jo-Wilfried Tsonga in straight sets, but the pair had an on-court spat early in the match. Photograph: Issei Kato/Reuters

Now Federer looks to the greater challenger of the friend and rival he has known and practised with for most of his career. Wawrinka played to his world No4 ranking in defeating the 12th seed Jo-Wilfried Tsonga, 7-6, 6-4, 6-3 in two and a quarter hours in the earlier quarter-final.

As close as they are, they will keep their distance in the locker room. They have had their differences, but those have evaporated soon enough, such as a post‑match row over an on-court interruption by Federer’s wife, Mirka, at the ATP World Tour Finals the week before they combined to win the Davis Cup for Switzerland for the first time in 2014.

They have mutual respect and understanding, if their lifestyles do not always cross. All of that will be forgotten when they step on to the court. Federer said later: “If someone would have told me I’d play in the semis against Stan, never would I have called that one. For Stan, yes, but not for me.”

He added: “I remember giving Stan a lot of advice on how he should play certain guys. What I like with Stan is, if I would tell him something, I felt like he was able to do it. That showed me that he’s a great player, that he’s got the mind of somebody who understands what I’m trying to explain to him.

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“Some players, you tell them something, they’ve just got no clue what to do, what it means. Stan had that early on – he was a great learner. Then the day came where he didn’t call me so much any more.”

After he beat Djokovic in the US Open final last year, Wawrinka was asked if Federer had offered him any advice beforehand. “In the past I talked many times with Roger,” he said courtside that night. “He asks me for advice. I ask him for advice. But, no, I didn’t ask him anything. I think I know exactly what I have to do now.”

And he will have a very clear idea of that on Thursday. He was at his belligerent best beating Tsonga – and even exchanging angry words with the normally unruffled Frenchman in the first set. Wawrinka has the uncanny knack of ignoring previous matches, good or bad – probably a trick he learned from Federer.

Federer says Wawrinka and Rafael Nadal are the two players with whose games he is most familiar. He has lost only three out of 21 against Wawrinka and blitzed him in their only contest here, in the quarter-finals eight years ago. But the question that lingers in every meeting with Federer is: how long can he extend his glorious career?

“I will probably never be able to play 27 tournaments a year any more,” he said, reflecting on his long break last year. “We all know that. But, maybe instead of playing 22, you play 18, instead of 20 you play 17. That could totally happen. You always need the right balance, I feel like, enough practice, enough matches, enough time off. I guess as you get older, everything becomes a bit different.”

Yet some things, like that peerless Federer forehand, the ridiculously easy passing shot and the single-handed backhand on which he does not release the trigger until the last possible second, do not really ever change. They just don’t arrive as often. In Melbourne the past nine days, they have been welcome guests again.