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In a titanic struggle played out over four hours and 43 minutes, world number one Djokovic squandered two match points in the fourth set tiebreak before going on to seal a final clash against either British second seed Andy Murray, the runner-up last year, or 24th seeded Pole Jerzy Janowicz.
The top-seeded Serb, bidding for a seventh Grand Slam crown, fired 22 aces and 80 winners against the luckless Del Potro, the 2009 US Open champion.
"It was one of the best matches I've been part of, certainly one of the most exciting. It was so close and nothing could separate us," said Djokovic.
"But that's why he is a Grand Slam champion, every time he was in a tough situation he comes up with unbelievable shots.
"I'm very proud to go through. When I lost the fourth set of course it was disappointing because I was close to winning and didn't capitalise. He came up with some big forehands. It was a very high level of tennis.
"I was ready to go five sets. I was able to stay tough and get through in the end."
Del Potro said he had played his best match on a grass court.
"I was so close. I played really good tennis for four and a half hours but he hits the ball so hard. I am sad because I lost," said Del Potro.
"It was just a couple of points, it was my best tennis on grass but against the world number one it's not enough.
"Novak runs like he's playing on a clay court or hard court. Always the ball comes back. He deserved to win."
Del Potro, who had defeated the Serb for the Olympic bronze medal at Wimbledon last year, matched Djokovic blow for blow in the first set but had to bat back a break point in the sixth game to stay on level terms.
At 6-5, Djokovic stepped it up, a backhand from off his toes landing in the corner before a backhand off-balance from the Argentine sailed long.
The Serb, playing in his fourth successive Wimbledon semi-final, sensed blood and a wide forehand from the suddenly besieged Del Potro gave the world number one the opener.
Del Potro called for the doctor after slipping down 3-2 in the second set, but the consultation didn't remedy his problems against the top seed as he immediately had to fend off four break points.
However, buoyed by his defiance, Del Potro broke for a 4-3 edge, the second point of the game clinched by chasing down a Djokovic drop shot which he dinked over cross-court.
Del Potro just about backed it up for 5-3 before he went on to level the tie, a picture-perfect drop shot followed by an unreturned serve.
It was the first set that the Serb had dropped in the tournament.
Djokovic fought off a break point in the fifth game of the third set and two more in the seventh before the Argentine had to save three set points in the 12th, the last courtesy of a 90mph winner.
Djokovic cruised through the tiebreak with Del Potro's confidence and challenge shattered in an instant when the 6ft 6in (1.98m) giant netted an easy smash on the sixth point.
Del Potro was beginning to wilt in the 26-degree heat and Djokovic took advantage, breaking for 4-3 as another fierce return landed on the Argentine's toes.
However, Del Potro brought the crowd to their feet by breaking back for 4-4 and saving two match points in the breaker, the first at the end of a punishing 24-stroke exchange.
In the decider, Djokovic fought off a break point in the fifth game before Del Potro saved one in the sixth.
The Argentine cracked to trail 3-5, Djokovic saved another break point as he served for the match in the ninth game before he claimed his epic win with a huge forehand.
Wimbledon results on Friday, the 11th day of the 2013 tournament (x denotes seeded player):
Men's singles:
Semi-finals:
Novak Djokovic (SRB x1) bt Juan Martn Del Potro (ARG x8) 7-5, 4-6, 7-6 (7/2), 6-7 (6/8), 6-3
Andy Murray (GBR x2) bt Jerzy Janowicz (POL x24) 6-7 (2/7), 6-4, 6-4, 6-3
Women's doubles:
Semi-finals:
Hsieh Su-Wei/Shuai Peng (TPE/CHN x8) bt Shuko Aoyama/Chanelle Scheepers (JPN/RSA) 6-4, 6-3
Ashleigh Barty/Casey Dellacqua (AUS/AUS x12) bt Anna-Lena Groenfeld/Kveta Peschke (GER/CZE x7) 7-6 (8/6), 6-2
Mixed doubles:
Semi-finals:
Daniel Nestor/Kristina Mladenovic (CAN/FRA x8) bt Nenad Zimonjic/Katarina Srebotnik (SRB/SLO x3) 6-2, 6-7 (4/7), 11-9
Bruno Soares/Lisa Raymond (BRA/USA x1) bt Jean-Julien Rojer/Vera Dushevina (NED/RUS) 6-4, 6-4
