Current number one Halep made the semi-finals for the third time by battling past Germany's Angelique Kerber 6-7 (2), 6-3, 6-2.
However, when the players came back on after a delay of nearly an hour Nadal immediately broke back to level the second set.
Nadal had won 37 consecutive sets at Roland Garros since his 2015 quarter-final defeat by Novak Djokovic but dropped serve three times to the enterprising Schwartzman in an exciting opener.
Nadal patted Marterer sympathetically on the chest at the net after winning on his second match point.
Nadal had to receive treatment to his wrist at the end of the set with extra strapping applied.
Play will resume on Thursday, with both matches finely poised.
He may have halted the mutiny for now but Nadal was strangely off-colour, unable to dictate the rallies as he usually does on clay.
Play continued though, with the set following a similar pattern to the first, as Nadal broke back before dropping his serve to 15.
Schwartzman's supporters will be hoping he won't be too exhausted from his heroic five-set win over the giant South African Kevin Anderson on Monday and has the self-belief to overcome a 0-5 head-to-head record against Nadal.
More important than that, of course, is the match's ultimate outcome, and a significant moment came with Schwartzman serving while up 3-2 in the second after the initial delay.
But Schwartzman was in no mood to give up and broke the Spaniard twice in the seventh and the ninth game, with Nadal earning a break of his own in the eighth.