Serving for the set, Schwartzman missed two set points before he saved a break-point of his own.
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.
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.
Russian crude oil output stagnant but remains above quotas in May
It has doubled in less than a month, as a lack of pipeline capacity in the U.S. has trapped a lot of output inland. West Texas Intermediate and international-benchmark Brent crude oil futures are trading lower early Monday.
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.
Spaniard Nadal, bidding for an 11th title on the Parisian clay, also trailed by a break in the second set as Schwartzman threatened a huge shock, but after a rain stoppage, Nadal returned to court to move 5-3 ahead in the second set.
Kasatkina raced away with the last three games of the tie which had been halted at 3-3 in the second set late Sunday because of bad light.
With Halep having outlasted Angelique Kerber on Wednesday, 6-7 (2-7), 6-3, 6-2, then looked at her coach while pointing to her head, she and Muguruza grace the bracket opposite the all-American match between Sloane Stephens and Madison Keys, the 2017 US Open finalists who have their own curious paths.
Trump hints at bilateral deals with Canada, Mexico
Mexico also responded to the taxes, saying it would impose tariffs of its own, and the European Commission promised legal action. All six of the other G7 countries are now paying the tariffs, which are largely aimed at curbing excess production in China.
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.
Play continued though, with the set following a similar pattern to the first, as Nadal broke back before dropping his serve to 15.
The Romanian broke serve six times against a player who made the semi-finals at the Australian Open in January.
Trump lawyer Giuliani says president can probably pardon himself
Mr Giuliani, the head of Mr Trump's legal team, said he " probably does", but added: "He has no intention of pardoning himself ". Both Russia and Mr Trump deny collusion, and the President has denied obstructing the probe.