The fifth seed had led by two sets on Monday but Simon grabbed the third set before fading light ended play.
With world number one Rafael Nadal waiting for the winner, Tuesday’s fourth set, played in much cooler conditions than the first three the day before, turned into a mini-epic before Del Potro eventually prevailed 7-6(1) 7-6(5) 5-7 7-6(5).
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. He looked on the brink of victory when he moved 40-15 ahead but both match points vanished, the second with a double-fault.
Simon failed to convert a break point, then a third match point for Del Potro ended with him netting a forehand. The 33-year-old Simon saved a fourth match point when he threw the kitchen sink at a forehand return and the world number 53 eventually took his fourth break point to level at 5-5.
The next two games went with serve and the match was well into its fifth hour when the tiebreak began.
Del Potro trailed 1-3 but at 5-5 he fired down a swinging ace to reach match point number five and this time Simon cracked, netting a backhand to the relief of the Argetine who roared his approval.