The match suffered as a result of two long rain delays, but the Argentine progressed in four hours and 13 minutes, setting up a second-round match with Lleyton Hewitt.
After winning the first set 6-3, Del Potro dropped a second set after losing tiebreaker 7-5. However, he managed to restore his lead by winning the third set 6-4.
The former champion displayed awesome power and recovered well from a break down in the fourth as the Spaniard battled to force a decider.
For the second time in the match a tiebreaker was needed to separate the pair, but this time it was Del Potro who won 9-7 on his fourth match point.