Roger Federer has never been one to hide his emotions and the 36-year-old Swiss was in floods of tears here on Sunday after becoming the first man in history to win 20 Grand Slam titles. At the presentation ceremony Federer struggled to get through his speech after beating Marin Cilic 6-2, 6-7, 6-3, 3-6, 6-1 to win the Australian Open for the sixth time.

Federer famously broke down in tears here after losing to Rafael Nadal in the 2009 final – his only defeat in his record seven appearances in the final - and was again overcome by emotion here.

“Of course winning is an absolute dream come true,” Federer said as he addressed the crowd while holding his trophy. “The fairytale continues for me after the great year I had last year. It’s incredible.”

At that point Federer had to stop as the tears welled up. “We’ve had a wonderful time here in Australia,” Federer said. “We’ve had the best time as a family and a team.”

Still struggling to get out his words, Federer thanked the Australian country and people for their hospitality, particularly the fans at this tournament. “This is tough,” Federer said at the end before thanking his team. “I love you guys. Thank you.”

A remarkable standing ovation followed as the whole stadium rose to applaud Federer for several minutes while the big screens showed the tears rolling down his face. The watching Rod Laver was among those who got out their phones to record the occasion.

The greatest player of all time was made to work for his latest triumph but if anyone had any doubts as to whether he could repeat his extraordinary feats of last year, when he won two Grand Slam titles upon his return from a six-month break because of injury, they were surely erased here.

At 36 years and 173 days Federer is the oldest male winner of a Grand Slam title since Ken Rosewall won here in 1972 at the age of 37 years and 62 days. With his 20 Grand Slam triumphs – four more than Nadal, the next player on the all-time list – Federer has won 10 per cent of the tournaments contested since the open era began in 1968.

Cilic, nevertheless, pushed Federer hard. The Swiss had won his first six matches here in straight sets but there were times in the final when he wobbled under the pressure from Cilic’s huge ground strokes. Federer did not have the best serving day and sometimes looked vulnerable on his backhand but, as usual, showed extraordinary mental strength whenever his back was against the wall.

While Nadal and Federer will remain at No 1 and No 2 in Monday's updated world rankings list, Cilic will climb to a career-high position at No 3.

Cilic had lost eight of his nine previous meetings with Federer, including last summer’s Wimbledon final, when the 29-year-old Croatian was reduced to tears after a painful foot blister scuppered his chances.

Federer had also won their most recent encounter at the ATP Finals in London in November, though the last time they had met on the court was only last month when they practised together in the Maldives after finding out quite by chance that they were both holidaying on the islands.

After a hot and humid day the referee decided to play the final with the roof over Rod Laver Arena closed, though it was not clear whether that decision followed the tournament’s own guidelines.

The Australian Open’s “extreme heat policy” appeared to suggest that it could be invoked only when the temperature topped 40C and the “Wet Bulb Globe Temperature”, which takes into account humidity, exceeds 32.5C. According to weather reports, the temperature during the day never exceeded 38C. Ultimately, however, the decision on whether to invoke the policy is at the referee’s discretion.

While it was true that the conditions were the same for both men, Federer has long had a reputation as the game’s best indoor player. Greg Rusedski, writing on Twitter, called the decision “absolutely ridiculous”, pointing out that Grand Slam tournaments are meant to be outdoor events. “Yes it’s hot but the court is under shade and [it’s] an evening match,” the former world No 4 wrote.

Federer was immediately into his stride. By the time he had gone 4-0 up in just 13 minutes he had won 16 of the first 20 points. Cilic changed his racket in the third game but it did not do him much good.

The Croatian finally got on the scoreboard in the fifth game, to some ironic cheers from the crowd, but within 24 minutes Federer had wrapped up the first set, completing the job with two aces followed by a service winner.

Cilic had at least started to play himself into contention and in the second game of the second set forced his first two break points. Federer, however, saved both. There were no breaks of serve in the set, though Federer had break points in the third, fifth and ninth games and Cilic had another in the tenth.

In the tie-break Cilic went 6-4 ahead with a huge forehand winner to the corner and on his third set point he clenched his fist in celebration after hitting a winning smash.

Cilic needed to keep the momentum in his favour, but at 2-3 he played a loose service game as Federer broke to 15. Federer served out for the set by holding to love, completing the job with an ace.

The Swiss immediately rubbed salt into Cilic’s wounds by breaking in the opening game of the fourth set after the Croatian lost the last two points with lame backhands.

Many in the crowd might have been expecting Federer, one of the game’s great front-runners, to close out victory with minimal fuss, but at 3-2 he dropped serve in unlikely fashion. The Swiss went 0-40 down with his fourth double fault and Cilic won the next point with a crunching forehand return.

In the eighth game of the set Cilic broke again as the Croatian thundered some huge returns into his opponent’s feet. When he served out to love in the following game to level the match at two sets apiece the crowd’s reaction was largely one of stunned silence.

When Federer saved two break points in the opening game of the fifth set he appeared to be teetering on the brink, but at deuce in the next game he successfully challenged an “in” call on a second serve - to huge roars from the crowd - and broke on the next point when Cilic netted a forehand.

At 4-1 Cilic dropped serve again when he netted a forehand on break point, which gave Federer the opportunity to serve out for victory. On his first match point Federer hit a superb kicking second serve wide to Cilic’s backhand which the Croatian was unable to return.

Cilic challenged in the hope that the serve might have been out, but the video replay showed that the ball had just clipped the line. The margin was certainly smaller than the gap that now separates Federer from all his rivals in the history of this sport.