Tsitsipas has made a disappointing start to the season, but took just 71 minutes to dispatch Ymer 6-1 6-3 on Wednesday.
The ATP Finals champion lost just three points on his first serve and did not face a solitary break point in an emphatic win.
Second seed Tsitsipas will face Vasek Pospisil in the last eight following the Canadian's 6-3 6-4 defeat of eighth seed Hubert Hurkacz.
Sixth seed Benoit Paire made a surprise exit in his homeland, going down 3-6 6-4 6-4 to Alexander Bublik in the second round.
It was anything but plain sailing for Felix Auger-Aliassime, who saved two match points before getting past Stefano Travaglia 6-7 (3-7) 7-6 (8-6) 6-3.
Auger-Aliassime's second-round opponent will be Pierre-Hugues Herbert, a 7-6 (7-4) 6-4 victor in his match against Mikhail Kukushkin.
Egor Gerasimov also reached round two by knocking out fellow qualifier Dennis Novak.
American Korda had never played a main-draw match on clay prior to the tournament and the gulf in class was evident throughout as Nadal barely broke sweat in the swirling gusts.
The 'King of Clay', aiming for a 13th title in the French capital, has dropped just 23 games in four matches thus far but 48 unforced errors from Korda, a huge Nadal supporter growing up, helped his cause on Court Philippe-Chatrier.
"I honestly believe we are looking at a great player, he had some mistakes in important moments but the way he hit the ball is impressive," said a gracious Nadal, who has reached the last eight without dropping a set for the eighth time. "I'm happy to be in the quarter-finals again and [it was] another tough match today."
Korda was such a big fan of Nadal's he named his pet cat 'Rafa' and the giant American got his claws into his opponent early with a couple of break-point chances.
But, having seen them off, Nadal was soon purring. With Korda - who was hindered by 18 first-set errors - struggling in testing conditions, he Spaniard breezed through the opener in just 40 minutes.
Nadal only hit nine winners in the first two sets as Korda's error count continued to creep up but one particularly wonderful textbook forehand down the line set up another break and a two-set lead.
To his credit, Korda made a decent fist of it in the fourth, taking a 2-0 lead early doors, only for an unflappable Nadal to reel off six straight games and coast into the last eight.
Data slam: Nadal punishes error-strewn Korda
It would have taken a huge leap of faith to back Korda in this one but an error count of 48, even accounting for tricky conditions, is a gift you cannot present Nadal no matter how much you admire him.
That Nadal, who won 64 per cent of points at the net and was successful with 72 per cent of second serves, had just 15 winners tells the story of how he did not need to hit top gear.
WINNERS/UNFORCED ERRORS
Nadal - 15/20
Korda - 21/48
ACES/DOUBLE FAULTS
Nadal - 1/1
Korda - 0/2
BREAK POINTS WON
Nadal - 8/11
Korda - 1/6
Italian Travaglia has a surname that translates to mean 'troubles', but Nadal was given no real cause for concern in a 6-1 6-4 6-0 victory.
Such was his control that the Spaniard won 82 per cent of points on his second serve, higher than his first-serve rate.
"I played my best match so far this year at Roland Garros. I hope I can play this way until the end," Nadal said in an on-court interview.
These early rounds are more important than usual for Nadal, who arrived in France short of match activity after sitting out the Western and Southern Open and the US Open.
Although he returned to action at the Internazionali d'Italia in Rome, that was his first tournament since February, and a quarter-final exit to Diego Schwartzman was a worrying setback for the greatest clay-court player in history.
Step by step, Nadal is going through the gears in Paris, the 12-time champion inching towards the form that has brought him such rich rewards on previous visits to the French capital.
To win a 13th title at this tournament, which would move him level with Roger Federer's all-time men's record of 20 career grand slams, Nadal is likely to have to beat Dominic Thiem in the semi-finals and Novak Djokovic in the title match.
Travaglia had some spark to his game, and he played a number of clever shots that made the second set a contest, but few have ever had the tools to stop Nadal on this surface and the world number 74 was inevitably found wanting.
Next for Nadal is a last-16 clash with Sebastian Korda, the American son of former French Open runner-up Petr Korda.
Data slam: Volley good show from Nadal
It ended with a volley, and Nadal was often coming in close, winning 19 of 23 points where he attacked the net. He won six of seven break points and said afterwards that it was his most aggressive performance so far this fortnight. The serving is looking good, he remains a baseline master, and the fact Nadal is marauding front and back of the court augurs well for what lies ahead.
WINNERS/UNFORCED ERRORS
Nadal - 28/13
Travaglia - 13/24
ACES/DOUBLE FAULTS
Nadal - 2/0
Travaglia - 1/1
BREAK POINTS WON
Nadal - 6/7
Travaglia - 0/0
