The 22-time Grand Slam champion is through to the last four of a tournament for the first time since Wimbledon two years ago.
"It was very close, long and tiring," said Nadal, whose near four-hour victory was the second longest three-set match of his career -- after the 2009 Madrid semi-final against Novak Djokovic, which lasted 4hr 3min.
"For moments he was in control. For moments I was in control. At the end, no one was in control. That's the truth," added Nadal.
"I was able to hold physically till the end. Let's see how I am tomorrow. Today I'm alive and I'm in the semi-finals. So that's super important."
Nadal had to overcome a poor start against the fast-rising Navone, now ranked 36th in the world after beginning the year outside the top 100.
He dropped serve three times in a row against an opponent who became the first man in the Open era to be seeded in his maiden Grand Slam appearance at this year's French Open.
The Spaniard trailed 4-1 and was down a double break but battled his way back into the set, saving two set points in the 10th game before eventually moving 6-5 ahead.
Nadal himself had two set points as Navone served to stay in it, the fourth seed showing his mettle to force a tie-break in which he won the first five points to take charge.
Back and forth
Navone secured the first set when Nadal sprayed a forehand wide, but the Spaniard quickly regrouped and raced into a 3-0 lead in set two.
His advantage was swiftly erased though by Navone who pocketed four games on the spin before Nadal stopped the rot.
Navone held to put the pressure back on Nadal, the 2005 Bastad champion, but the 38-year-old didn't flinch, winning his service game and then breaking for a 6-5 edge.
He sent the contest to a decider after sealing the set with an emphatic smash and celebrating with an animated fist pump.
Navone nudged 2-0 ahead in the third set before Nadal hit back with authority, sweeping five successive games before a late stumble allowed his rival to haul himself level at 5-all.
But Nadal broke again and finally crawled over the finish line when Navone dumped a forehand return into the net.
Nadal will next face Croatian qualifier Duje Ajdukovic, the world number 130 who had won just two tour-level matches in his career prior to this week.
The 23-year-old Ajdukovic beat Brazil's Thiago Monteiro in three sets in the quarter-finals.
Nadal won the last of his 92 singles titles at the 2022 French Open, as he claimed a record-extending 14th Roland Garros crown.
He is using the event in Bastad as a tune-up for the Paris Olympics, where the tennis will be played at Roland Garros. Nadal returned to action this week for first time since losing in the first round of the French Open in late May.
Nadal is also still involved in the doubles in Sweden, where he is teaming up with Casper Ruud. They are due to play in the semi-finals on Saturday, after Nadal plays his singles match.
"It's time to work on the recovery. Let's see how I am tomorrow," he said.
