It was a tight contest between the pair, who pushed each other to the wire in the early stages of the first set, but Nieminen's swift returns allowed him to nab a vital break of serve.
Nieminen took control of the clash by that point, blasting powerful forehands and quick movement around the clay court to take a one-set lead over his Argentinian opponent.
Del Potro responded in the second set by snatching an early break and managing to hold to give himself a strong advantage over Nieminen, who struggled to answer Del Potro's strong shots.
After drawing level on sets, Del Potro had numerous break points to give himself the lead, but he squandered his chances, which allowed Nieminen to nab a break himself to go on top.
Despite taking the advantage, Del Potro immediately responded to draw level on games in the final set and later snatched his own break, but Nieminen continued to match his opponent and eventually a tie-break was needed to decide the contest.
While both players battled to get the win, Nieminen came out on top in the head-to-head to set up a quarter-final match against Novak Djokovic.