Sinner drew level in the set but repeatedly had to lean on his racket between points, and after winning game six, was visibly out of breath in his seat, looking out of breath as he conceded the second set.
But Medvedev started to make mistakes of his own, hitting two consecutive double faults in giving up his serve in game three of the third set, as Sinner took control before the rain stopped play.
Sinner is still the favorite to become the first Italian to win the Rome title in five decades, ahead of a potential career Grand Slam at the French Open.
Should he get to the final, he will have to get past Ruud, who reached his first title decider since winning in Stockholm in October last year by dismantling Luciano Darderi 6-1, 6-1, another match interrupted by heavy rain.
Ruud, a clay specialist, dealt with flamboyant Darderi with the minimum of fuss, even with a downpour that forced him to wait nearly two hours to restart a match he was already winning easily.
The Norwegian hasn’t won a single set in any of his four matches with Sinner and was destroyed 6-0, 6-1 by him in the last eight last year in one of the most one-sided matches ever seen at the Foro Italico.
“It will be a tough match no matter who it is,” said Ruud after his match.
“If it’s Jannik, it will be another test for me, and hopefully I can get some sort of revenge from last time we played.”
When play was stopped, Ruud was 4-1 up and at an advantage in game six of the first set, which he immediately won after the restart on center court in Rome.
Not including the rain interruption, Ruud took little more than an hour to see off Darderi to win a tour-leading 140th match on clay since the start of 2020, in which time he has won more tournaments on the surface than any other ATP player.