ATP World Tour Finals 2013: Roger Federer sets up semi-final with Rafael Nadal after coming from behind to beat Juan Martin del Potro

Roger Federer has won more matches than anyone at the Barclays ATP World Tour Finals but few can have been more dramatic than his 44th victory here at the year-ending championships.

Needing to beat Juan Martin del Potro to reach the semi-finals for the 11th time in 12 appearances, the 32-year-old Swiss repeatedly had to dig himself out of trouble before winning 4-6, 7-6, 7-5.

Federer, who was 3-0 down in the third set, may have had his least successful season for 12 years but he showed that the old magic is still there, even if we see it less frequently these days. The world No 7 faces Rafael Nadal in a semi-final to be savoured this afternoon before Novak Djokovic – a 7-6, 4-6, 6-3 winner over Richard Gasquet – takes on Stanislas Wawrinka.

The capacity 17,500 crowd, who were overwhelmingly behind Federer, were treated to the best match of the week in a winner-takes-all shoot-out for the last semi-final place. It was a match that summed up Federer's year. There were times when he looked a spent force, frustrated by his mistakes, but others when he was as majestic as ever.

"I fought back the whole match," Federer said afterwards. "I was really getting angry at myself, wondering how I could just play a loose game, wondering why this was happening.

"I wasn't in many of Juan Martin's service games, so I felt I would probably get just one more chance to break back [in the third set]. That's exactly what happened. Once on even terms, I was able to play a little bit more freely. For the first time I almost felt like I was in the lead. It was a great finish. I was very happy. To get the victory was a great feeling."

Del Potro went 5-1 up in the opener before Federer embarked on a masterclass. The Swiss won 16 out of the next 20 points and went within a point of levelling at 5-5 after a rally of sheer brilliance.

Under attack, Federer hit an exquisite sliced backhand lob into a corner and followed it up with a winning volley. Del Potro, nevertheless, served his way out of trouble to take the set.

The world No 5 again drew first blood in the second set, only to play his worst game to allow Federer to break back for 3-3.

The Swiss went on to play an excellent tie-break, clinching it 7-2 with an ace. Once again magic was followed by mediocrity as two woeful Federer forehands enabled Del Potro to make the first break of the decider, but the former world No 1 clawed his way back to 3-3 from 3-0 down.

By now the pair were playing some breathtaking points. In one, Del Potro retrieved a lob with a through-the-legs "hot dog" before Federer, chasing another lob, hit a wonderfully improvised overhead with his back to the net and then won the point with a forehand cross-court pass.

At 5-5 Federer made the final break, forcing Del Potro into a mistake with a splendid return. Federer saved one break point in the next game before sealing victory with an ace, upon which he thrust his arms in the air and beat his chest in celebration. There is clearly life in the old dog yet.