At the start of the Australian Open, Stanislas Wawrinka said he did not need to win a grand slam title to regard himself as a success.

The Swiss has lived the majority of his career in the shadow of Roger Federer but, at the age of 28, and after knocking out Novak Djokovic in an epic quarter-final last night, he is just two wins away from fulfilling a dream.

Tomorrow, he plays the Czech Tomas Berdych for a place in his first grand slam final, his just rewards for never giving up hope, even in an era when Federer, Rafael Nadal, Djokovic and, more recently, Andy Murray have cleaned up all the sport's biggest titles.

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The tattoo on his arm is a quote from Samuel Beckett: "Ever tried. Ever failed. No matter. Try again. Fail again. Fail better."

It could not be more apt for Wawrinka, especially in relation to Djokovic, who beat him in two heartbreakingly close five-set battles last year, here and in the semi-finals at the US Open.

The Serb looked likely to repeat the feat last night when he broke to lead 2-1 in the final set but he handed the break straight back before Wawrinka broke to win 2-6, 6-4, 6-2, 3-6, 9-7 in a match of stunning shot-making, much of it from the Swiss.

A new alliance with coach Magnus Norman, which began last April, has worked wonders for his confidence and, for the first time, he really believes that he belongs on the biggest stage.

"I now trust myself when I go on court," he said after beating Djokovic. "I know that I can beat those players. Even when I lose, I go back to practice, to try to improve. That's my line in general in my tennis career, so I will keep going and doing the same things."

With a free-flowing one-handed backhand that had many of his fellow professionals purring on Twitter yesterday, Wawrinka has always been a pleasure to watch. But it took Norman, the former world No.2 and a French Open runner-up, to turn him from a huge talent into a true believer.

"He did an amazing job with Robin Soderling, taking him from 30 to top five," Wawrinka said. "We were a little bit similar last year, what I did and what he did with Robin. Robin was better so far, but I'm really happy. We had more or less the same vision of tennis; we know it all comes from the practice. So far it's been great."

Belief is one thing but doing it is another and, against Djokovic, Wawrinka never let his head drop, never showed the Serb that he was hurting as the cramps set in.

Bold, aggressive hitting kept the world No.2 off balance and his serve, occasionally an area of weakness when the Swiss is not at his best, was a revelation, digging him out of trouble on several occasions.

Wawrinka beat Murray at the US Open last year - having done the same thing in 2010 - but admitted seeing one of the big four win almost all the grand slams was difficult to cope with. "They are just better players than us, than all the rest," he said. "They are just amazing fighters, amazing players. That's why they always won everything.

"But I think last year I took a lot of confidence from those matches with Novak. I was really close. I was playing good. I came on the court knowing that if I play my best game, I always have a chance against him."

Having won six of the past seven matches with Berdych - he upset third seed David Ferrer of Spain in four sets yesterday - Wawrinka might just be favourite for their semi-final, but he intended to enjoy his win over Djokovic before thinking too far ahead. "I'm still far from winning the tournament," he said. "Two matches, the most difficult matches."

Berdych has enjoyed more attention this week than normal, if only for his blue-and-white striped Kilmarnock-style tennis shirts, but the Czech is playing some of his best tennis and will fancy his chances of reaching his second grand slam final.

The women's game, meanwhile, may just have found a new star. Eugenie Bouchard, the Canadian teenager and former junior Wimbledon champion, reached her first grand slam semi-final after wearing down an injury-hit Ana Ivanovic 5-7, 7-5, 6-2, the Serb unable to follow up her shock win over top seed Serena Williams.

Bouchard is set for the top and is equally assured off the court as she is on it. "I try to stay calm and focused and do my thing," she said. "It's not surprising to me to be in the semi-final because it's what I've been working for."

Getting to the final, though, will not be easy with China's Li Na, the runner-up here in 2011 and again last year, standing in her way. The third seed looked in good form as she saw off Italy's Flavia Pennetta 6-2, 6-2.