Poland's top seed Swiatek set up the blockbuster meeting when her ailing fourth-round opponent Lesia Tsurenko of Ukraine retired while down 5-1 in the first set after she called the physiotherapist and had her blood pressure checked.
Gauff won her previous clash with Schmiedlova in Madrid last year, dropping only two games, and the American made a quick start again with a break in the opening game to pull away and leave her 100th-ranked opponent facing an uphill task.
But Schmiedlova, playing in the second week of a major for the first time, mounted a late fightback from 5-2 down in gusty conditions to draw level only to squander her chance and allow sixth seed Gauff to edge a tense first set.
"Today was honestly a difficult match, as every match is. But the wind was something that, I don't know, I wasn't really that prepared for it going in," Gauff said of conditions on Court Philippe Chatrier.
"The one side was gusting like really crazy. Usually, I like to play in the wind, to be honest, but it wasn't something I was prepared for. Overall I'm happy with how I played."
She tightened her grip in the second set, working the angles and deploying the drop shot to devastating effect as she closed out the win without any more drama.
Gauff is relishing a rematch with world number one Swiatek.
"Since last year, I've been wanting to play her, especially, at this tournament," the American said shortly before Swiatek went through after just 31 minutes.
"I figured it (a meeting) was going to happen because I figured I was going to do well and she was going to do well... if you want to be the best you have to beat the best.
"If you want to improve, you have to play the best. The way my career has gone so far, if I see a level and if I'm not quite there at that level, I know I have to improve. You don't really know what you have to improve on until you see that level."
Swiatek through after Tsurenko retires unwell
Defending champion Swiatek needed only 31 minutes to reach the French Open quarter-finals on Monday as her Ukrainian opponent Tsurenko retired after feeling unwell.
World number one Swiatek was 4-1 up in the opening set when Tsurenko called on the trainer and had her blood pressure and pulse checked.
Following a five-minute medical timeout, the match resumed but Tsurenko threw in the towel after losing the following game to love.
"I'm sorry, playing Iga was my priority, I'm very sorry," Tsurenko told a press conference.
"I've had this virus for a couple of days and today it was tough for me to warm up and I hoped I would feel better during the match but unfortunately it got worse. My body could not take it.
"I was fine at my last match although I started to have a sore throat and then yesterday I could practice for only 10 minutes. I had litres of water and healthy things, vitamins, a lot of fruits. I need another two, three days to recover."
Wearing a ribbon in the Ukrainian colours pinned to her cap while Tsurenko had one on her top, Swiatek raced to a 4-0 lead as the world number 66 started to show signs of weakness.
She still managed to pull a break back but requested the trainer to come on court as she sat down on her bench at the change of ends.
She was seen explaining her problems to the medical staff and after being given the green light to continue, it soon became evident that she was struggling to play her shots and ended the match prematurely.
Swiatek has dropped only nine games en route to the quarter-finals as she chases a third Roland Garros title in four years.
"Obviously it's not the way you want to win a match," Swiatek told a press conference.
She, however, was satisfied with her campaign so far as she can now rely on experience to deal with the demands of a Grand Slam.
"Before I was exhausted mentally and physically, every match cost me a lot but now I'm able to do better," she explained. "In the first part of the tournament, it's important to keep something for the next round."
Swiatek is now well-established as a top player and reaching the quarter-finals at a Grand Slam gives her little to celebrate, although that does also depend on the major.
"If I could be in the quarter-finals at Wimbledon I would be over the moon," she said with a laugh.
