Nadal was back on serve immediately when the exuberant underdog put too much on a groundstroke, but Schwartzman regained the advantage with a simple volley to lead 4-3 after toying with the Spaniard.
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's last win after losing the opening set came against Novak Djokovic in the 2014 final.
But the 16-time major victor 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'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.
However, when the players came back on after a delay of nearly an hour Nadal immediately broke back to level the second set.
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. As the game was stopped for two minutes, Schwartzman walked back to his mark, amidst a huge cheer from the crowd, and took a set off the King.
Nadal broke back, yeah, sure, but then Schwartzman broke again, with an outrageous return that dove down inside the baseline and helped arrange a blasted forehand victor into the corner.
The freedom with which Schwartzman had played in the first set had disappeared, errors which had been rare becoming increasingly regular.
Play will resume on Thursday, with both matches finely poised.
The enforced interlude had clearly benefited Nadal, and assuming he gets the two points he needs to level the match he will start a strong favourite on Thursday.