The first set was a tight affair, with Thiem claiming the decisive break in the 11th game but the Italian retained his composure to send the second to a tie-break.
The second set, like the first, was dominated by serve until Cilic fired himself up to break at 4-4 - a furious Del Potro throwing his racket at the changeover. "I have a plan", a confident Thiem, who dispatched surprise package Marco Cecchinato 7-5 7-6 (10) 6-1 in the semi-finals on Friday, told reporters.
But Del Potro bided his time, applied some pressure at 5-5 and Australian Open runner-up Cilic cracked. That crucial early juncture altered the course of things, though. "He's one of the best players in the world on this surface", Nadal said.
"Just thinking in a positive way and just thinking that I have to hold". If he wins the game, OK.
"Even if it was 6-3 6-4, it was an uncomfortable match for me", Nadal said.
"I'm also aware that here it's tougher".
Nadal will face Austrian Dominic Thiem for the championship on Sunday, June 10.
Nadal crushed Del Potro's spirit with the intensity of his tennis in the second set, bounding 5-0 ahead before the Argentine registered a game to lift the spirits of his fans. He missed the tournament every year from 2013-16 because of injuries, including three operations on his left wrist.
Nadal and Thiem have met nine times - all of them on clay.
The 16-time major victor saw Schwartzman take a set off him in Paris for the first time since 2015, but Nadal survived a triple break-point before an injure scare to Del Potro appeared to swing the momentum away from the world number six. He gave Nadal a sound beating in Madrid, and whilst that has never been Nadal's favourite tournament - with suggestions that the relative altitude makes the ball travel faster through the air, dulling Nadal's usual advantages on clay - I'm inclined to view it as a sign of a growing equality on clay between the two of them. He has already won titles in Rome, Barcelona, and Madrid while the only loss came in the quarter-final of Madrid Open against fellow French Open semi-finalist, Dominic Thiem.
So, if a player as good as Thiem is on clay is still struggling for parity with Nadal, and there is no other obvious contender to trouble him, his path to at least 13 or 14 French titles would seem to be one covered in rose petals - if he stays healthy.
Romania's Simona Halep will first play American Sloane Stephens in the women's singles final tomorrow.
It is the second straight all-American girls' final at Roland Garros, after Whitney Osuigwe beat Claire Liu previous year.
He looked destined to be a multiple Grand Slam champion after winning the US Open as a 20-year-old, but nearly had to quit the sport because of career-threatening wrist problems.
Cecchinato's career has been tainted by his involvement in a match-fixing scandal; he was banned for 18 months in 2016 before having the suspension overturned.
Thiem got off the blocks quick with a break in the very firsts game after Cecchinato fought off with three deuces.
By the absurd standards Nadal has set here, even facing those break points amount to a lapse, as does the opening set he dropped to the terrier-like Diego Schwartzman in the quarterfinals.
Thiem weathered three set points for Cecchinato, at 7-6, 9-8 and 10-9.