Nadal quickly wrapped up the final two points needed to secure the second set and level the match before the world No 1 maintained his ascendancy during the third set with two breaks of serve to move ahead in the match, after saving four break points when he served out.
That game had a 40-15 lead for Schwartzman, a brilliant Nadal drop volley that rubbed out the second set point, a Nadal break point, a attractive duo of Schwartzman overheads for a third set point and, just then, after a first-serve fault, a spectator in the 15th row apparently fainting.
At one point Nadal, the reigning champion and 10 times victor, found himself a set and a break down to the diminutive Argentinian Schwartzman.
The Spaniard, who won five straight games after a rain delay to beat Alexander Zverev in the Rome Masters final last month, managed three in a row this time before play was ended for the day.
The 25-year-old took his third set point with a rasping forehand up the line, after being made to wait when a spectator fell ill in the stands.
Schwartzman failed to consolidate the break again, but was undeterred as a ferocious forehand victor put him 5-4 up, and another fizzed forehand victor ended Nadal's long run of sets won in a row in Paris after a stoppage when a spectator collapsed.
He led 30-15 when play ended at 18:37 BST, returning at 11:00 BST on Thursday to wrap up the set and level in a matter of seconds.
Two-time runner-up Halep came back from a set down for the second time in the tournament to see off 12th seed Kerber, who was bidding to become the first German woman in the last-four since Steffi Graf in 1999.
Schwartzman had a point to lead 4-2 but a forehand error allowed Nadal off the hook.