Amazingly, irresistibly, beguilingly Roger Federer is playing tennis, five months short of his 36th birthday, that, apart from minor adjustments for age, is virtually indistinguishable from that which held his rivals transfixed for most of his 20s. It hardly seems possible but it is happening.

There were plenty of observers, one of them not far from this keyboard, who doubted Federer could break the long spell he endured without a major after beating Andy Murray at Wimbledon in 2012. True believers in the press pack were confined to a knot of shameless sycophants.

It did not make sense that Federer could break the strengthening duopoly of Novak Djokovic and Andy Murray, even though the Swiss twice pushed the Serb close at Wimbledon, once in a classic final, in 2014. Rafael Nadal, too, from time to time was still in front of him. Federer resembled a fallen Hollywood star who kept auditioning for the same role while the greasepaint ran embarrassingly down his cheeks.

But on Sunday evening, only a few hours after a chronically painful right elbow forced Djokovic to join Murray on the injured list and withdraw from the forthcoming Miami Open, the ageless Federer beat 31-year-old Stan Wawrinka to win the Indian Wells Open for a joint-record fifth time, 6-4, 7-5 in killing 34C heat over an hour and 20 minutes. It was as if he were rising again by sheer force of will.

Religious miracles are oceans parting and the lame throwing away their sticks. In tennis the earthly equivalent is Federer taking six months out in 2016 to recover from knee surgery that might have spirited him into retirement and returning to win this year’s Australian Open by coming from 1-3 down in the fifth set of the final, against Nadal, one of the game’s brutal finishers.

Not only has he broken his grand slam drought but he has blossomed like a cactus flower in the desert. Sunday’s victory in a tournament the organisers like to regard as the fifth major was short of that. These were best-of-three matches and there were five of them, not seven over a maximum of five sets, as in the majors. And Federer had a walkover against Nick Kyrgios in the quarter-finals. Still Federer, who held serve 37 times in a row to reach the final, did what he had to do. He was quick, sharp, smart, adventurous and merciless. He floated again and stung.

Federer is 19 short of the career collection of tournament victories of Jimmy Connors, who played in physically less demanding times. Connors quit tennis at 40. Federer, who said recently he might also play on until he is that age, began the week at No10 in the world but thinks he has an outside chance of returning to the top of the rankings, maybe even by the end of the year. There is gathering evidence to support a contention that seemed preposterous only a few months ago.

Murray, the world No1 since clambering over the worryingly brittle Djokovic towards the end of last season, is still favourite to hold his lead all the way to Wimbledon, where he will defend the title he won for the second time last summer. He said on Saturday he plans to be fit for the Monte Carlo Open, which starts on 16 April, although he made no mention of his commitment to Great Britain’s Davis Cup quarter-final against France in Rouen, which begins on 7 April.

The Scot picked up his complaint during practice in Indian Wells – where he lost his opening match to the world No129, Vasek Posposil – but Djokovic’s predicament, arising from a long-term problem that first surfaced after the French Open last year, sounds more serious. There were moments in his defeat by Kyrgios when the Australian almost knocked the racket from his right hand with his power-serving; few could recall that happening often in the same match.

Djokovic, unable to defend his Miami title and the points that go with it, risks sliding quickly away from Murray in the rankings unless he can regroup on the clay of Europe.

That anxiety could further eat into his confidence, which was stratospheric at the start of 2016. “My doctor has strongly advised against play because my elbow injury, that I keep carrying on for months, got worse in the past week,” Djokovic announced on his Facebook page.

“Sadly, I won’t be able to defend my title in Miami this week. Believe me, it is as shocking to me, as it is to you. I had [an] incredible run in Miami, I won there my first Masters tournament and started my campaign towards the top of the world rankings.

“No wonder they say that in sport the biggest and most painful defeats come from injuries and not from opponents.” Federer might yet have a say in that.