Cobolli started slowly in wild and windy conditions on Wednesday before beating Canadian fourth seed Felix Auger-Aliassime 4-6 6-4 6-4 6-4 to reach the semi-finals at Roland Garros for the first time.
Arnaldi then made it to his first grand slam semi after compatriot Matteo Berrettini retired from their quarter-final because of injury.
Following an early exchange of breaks, Auger-Aliassime pounced on Cobolli's serve in the 10th game to claim the opening set, after which the roof on Court Philippe Chatrier was closed.
Cobolli, one of three Italian men to make the quarter-finals after world No.1 and tournament favourite Jannik Sinner's premature exit, battled back from 1-3 down in the second set with the playing conditions suddenly improving.
"I think we played two different matches today," Cobolli said in an on-court interview.
"In the first set it was very windy and tough to play.
"I went to the toilet to think a bit. I tried to change something. I thought 'this is the best court I've played on in my life, because I can show my best tennis'.
"I said to myself to fight, this is the chance of my life and I must give everything in all my matches, so today I'm really happy.
"Tennis is like this, it changes every day. This week changed a lot and we have to be prepared, accept everything. I did it today and that's why I won this match."
Having levelled the contest at one set apiece, the 10th seed dialled up the intensity in the seventh game of the next set.
The 24-year-old thumped his chest when he edged ahead in the fourth set, and went on to comfortably secure the victory.
Cobolli said he was a superstitious person and would not change his routines.
"The tension of my racquet has been the same since two weeks, even with the warm weather," he said.
"I'll do my same routine today as every day, have dinner with friends. It's been the best week of my life, but I'm still missing something, so I have to fight again."
Cobolli's victory set up a semi-final with Arnaldi, who came out on top in an all-Italian clash after Berrettini retired injured while trailing 7-5 5-2.
Former Wimbledon finalist Berrettini, who needed a medical time-out for what appeared to be hip pain after three games in the second set, threw in the towel at the change of ends after being encouraged to do so by his entourage.
"It's a tough one,'' Arnaldi said.
"We both played a lot so it's normal to not be at our best, but you never wish someone's tournament to end like this.
"We're doing such a good job in Italy. I hope he recovers, the grass season starts soon and he's someone who is going to be tough to play against.
"I'm tired, that's for sure, but I train and play tennis and to play these tournaments, these matches."
Second-seeded German Alexander Zverev and Czech No.26 seed Jakub Mensik meet in the other semi-final.
- with AAP
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