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Nadal will tackle American 10th seed Mardy Fish, who he has defeated five times in five meetings, for a place in the semi-finals.
But his latest injury will be a major concern for the world No 1 Spaniard ahead of Wednesday's quarter-finals.
A dramatic first set, which saw him warned by umpire Carlos Ramos for taking too long between points, ended with the champion needing a medical time-out on Centre Court for a left foot injury at 6-6.
The 24-year-old had his foot bandaged while he sat in his chair, grimacing with pain, but still came out for the tie-break which he won even though his movement appeared to be restricted.
"I don't know what the problem is, it seems to be a problem with the bone in the foot," said Nadal.
"I thought I would have to retire at the end of the first set because there was a lot of pain. But the tape changed the situation. Now I will have to check with the doctors and the physios. Something is there."
Nadal, who had squandered two set points in the 10th game, had made Del Potro angry over the the amount of time spent on the attention paid to the Spaniard's injury.
A fired-up Del Potro then hit back to level the match, clubbing his way to the tie's first break in the eighth game of the second set.
The 22-year-old, who defeated Nadal for the loss of just six games in the US Open semi-finals in 2009 before he went on to clinch his first and only Grand Slam title, had never advanced beyond the third round here in three previous visits.
He missed last year's Wimbledon after a wrist injury, which restricted him to just three events and sent his ranking tumbling from four in the world to No 485 in January.
He is back at 21 now and was using his giant 1.98m (6ft 6ins) frame to hit deep and long on Monday.
But at 2-2, 15-30 in the third set, it was Del Potro's turn to suffer when he hurt his left hip in a nasty fall as he tried to switch direction to chase down a Nadal forehand on the baseline.
The Argentine, who had suffered a similar injury in Madrid in May, then left the court for a medical time-out before returning to the fray.
He kept swinging in the third set but was out-played again in the tie-break which he conceded with a tame forehand into the net.
Nadal broke Del Potro for the first time in the match to lead 3-2 in the fourth set and took the victory on his first match point when Del Potro went long with a lob.
Results from the seventh day of Wimbledon on Monday (x denotes seeding):
Men
Fourt Round
Rafael Nadal (ESP x1) bt Juan Martin del Potro (ARG x24) 7-6 (8/6), 3-6, 7-6 (7/4), 6-4
Mardy Fish (USA x10) bt Tomas Berdych (CZE x6) 7-6 (7/5), 6-4, 6-4
Andy Murray (GBR x4) bt Richard Gasquet (FRA x17) 7-6 (7/3), 6-3, 6-2
Feliciano Lopez (ESP) bt Lukasz Kubot (POL) 3-6, 6-7 (5/7), 7-6 (9/7), 7-5, 7-5
Jo-Wilfried Tsonga (FRA x12) bt David Ferrer (ESP x7) 6-3, 6-4, 7-6 (7/1)
Roger Federer (SUI x3) bt Mikhail Youzhny (RUS x18) 6-7 (5/7), 6-3, 6-3, 6-3
Bernard Tomic (AUS) bt Xavier Malisse (BEL) 6-1, 7-5, 6-4
Novak Djokovic (SRB x2) bt Michael Llodra (FRA x19) 6-3, 6-3, 6-3
Women
Fourth Round
Dominika Cibulkova (SVK x24) bt Caroline Wozniacki (DEN x1) 1-6, 7-6 (7/5), 7-5
Maria Sharapova (RUS x5) bt Peng Shuai (CHN x20) 6-4, 6-2
Sabine Lisicki (GER) bt Petra Cetkovska (CZE) 7-6 (7/3), 6-1
Marion Bartoli (FRA x9) bt Serena Williams (USA x7) 6-3, 7-6 (8/6)
Tamira Paszek (AUT) bt Ksenia Pervak (RUS) 6-2, 2-6, 6-3
Victoria Azarenka (BLR x4) bt Nadia Petrova (RUS) 6-2, 6-2
Petra Kvitova (CZE x8) bt Yanina Wickmayer (BEL x19) 6-0, 6-2
Tsvetana Pironkova (BUL x32) bt Venus Williams (USA x23) 6-2, 6-3
