Just 90 minutes after defending champion Roger Federer was sensationally knocked out by South African Kevin Anderson on Wednesday, it seemed as if the grasscourt major would lose its top two seeds as Argentine Del Potro took a two-sets-to-one lead.
The third set produced more high-quality tennis and Nadal was the first who crumbled under pressure, losing serve at love at 4-5 to drop another set and face an elimination.
And Nadal rued failing to take control against del Potro much earlier.
Del Potro looked flat as he was broken to trail 3-1 but he clawed his way back to lead 5-4 with his serve to come.
Del Potro fought back, but Nadal held again after the former wasted a break point.
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'In the third set he started to play better from the baseline and I had couple of mistakes with the game I lost.
In the next set, Del Potro broke and served for the set at 5-4, but double-faulted and Nadal clinched the break-back with a forehand victor down the line for the second set to be decided by a tiebreaker.
Soon enough, del Potro was down on his belly after one last slip, as Nadal finished off the victory with a volley.
But Nadal was first to break in the deciding set and he built a 5-3 advantage with a looped forehand victor before confirming his final four place with a volley after four hours and 48 minutes.
There was a look of glee in Del Potro's sometimes sad eyes, and his lumbering between-points walk had a bit more energy to it. Nadal, struggling to get a solid second serve into hard areas, was de-fanged for long stretches.
Nadal maintained his typically aggressive approach and was leaping while punching the air after a blistering return whistled past Vesely to put him a break up at 3-2 in the second set. Del Potro, who sprayed his once pained wrist with a powder on most changeovers, had new shoes brought to him after the seventh game of the fourth set.