Top seed Nadal, 32, trailed 6-4 3-5 when play was halted on Wednesday.
The world number one, bidding for a record-extending 11th title, clinched the second set soon after the restart.
And he lost just four games in an hour and 42 minutes on court on Thursday on his way to a 4-6 6-3 6-2 6-2 victory.
The Spaniard will face either Marin Cilic or Juan Martin del Potro, whose unfinished quarter-final was also moved over to Thursday, in Friday’s semi-final.
Whoever reaches the final from that side of the draw will face either Austrian seventh seed Dominic Thiem or unseeded Italian Marco Cecchinato in Sunday’s final.
Nadal is the hot favourite to win the second Grand Slam of the year after dominating on the red clay since making his Roland Garros debut in 2005.
But the 16-time major winner looked in danger of being beaten there for only the third time in his career, trailing a set and break on Wednesday to an opponent who had never previously been beyond the last 32.
Schwartzman started the match aggressively, hitting 20 winners as he became the first player to take a set off Nadal in Paris since 2015.
However, his fearless approach was completely ruined by the rain delays and allowed Nadal to regain control.
The match had already been stopped for an hour on Wednesday, with Nadal trailing 6-4 2-1, before play resumed at 17:28 BST.
The players only managed another 20 minutes on court before more rain forced them off for the night, but it was enough time for momentum to switch in Nadal’s favour.
Nadal returned with his famed forehand finally firing on all cylinders, earning back-to-back breaks to move within a hold of the set.
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.
Schwartzman is a rare sight in the modern men’s game, standing at just 5ft 7in, but his stature has not prevented him rising to a career-high 12th in the world rankings this year.
The 25-year-old Argentine possesses a stinging forehand and used it aggressively to rock Nadal on Wednesday.
On Thursday, it was rarely used as effectively.
From the moment Nadal took the second set, it looked unlikely Schwartzman would earn a first win in six attempts against the man at whose academy he had previously trained.
Nadal only dropped one point in the opening two games, going a double break up for a 4-1 lead.
Schwartzman missed four break points at 5-2 as Nadal eventually held serve to lead for the first time with three hours approaching on the clock.
The freedom with which Schwartzman had played in the first set had disappeared, errors which had been rare becoming increasingly regular.
An easy smash into the net midway through the fourth set characterised his problems, a total of 25 unforced errors compared to eight winners in the final two sets underlining the pressure being put on by Nadal.
Nadal, whose game was suited by the warmer and quicker conditions on Thursday, missed a match point on Schwartzman’s serve and spurned two more in the following game.
Schwartzman also missed three break points before his brief revival was ended when Nadal took his fourth match point to win in three hours and 36 minutes.