The 20-year-old needed 2hrs 47mins to get past a player 15 years her senior 7-5, 5-7, 6-3 ahead of the second rubber between world number nine Ashleigh Barty and two-time Grand Slam winner Victoria Azarenka.
Souza, who is currently languishing at 422 on the ATP rankings, was originally banned on March 29, but following a successful appeal he was reinstated on April 8.
The 11-time champion has not lost at the tournament since a 2015 semi-final defeat against Novak Djokovic and he now stands 71-4 at the event.
Medvedev will meet another Serb, Dusan Lajovic, on Saturday for a place in the final after the latter beat Italian qualifier Lorenzo Sonego.
Barty leads Australia's hopes of reaching a first Fed Cup final since 1993 when they face 2017 runners up Belarus in Brisbane.
Djokovic extended his winning streak against US players with a 6-3, 6-0 defeat of Taylor Fritz.
Stefanos Tsitsipas lost to Daniil Medvedev.
The 11-time champion showed no sign of the knee problems which forced him to quit ahead of an Indian Wells semi-final against Roger Federer a month ago.
The 11-time champion showed no sign of the knee problems which forced him to quit ahead of an Indian Wells semifinal against Roger Federer a month ago.
The German, who is based in the Principality, reached the third round with a comfortable victory over Felix Auger-Aliassime.
The Japanese star lost the Monte Carlo final a year ago to 11-time champion Rafael Nadal.
The winner of the last three Grand Slams made eight double faults, dropped serve four times and smashed a racquet after losing the second set to his German opponent in the second-round encounter.
Pella, who won his first career match at the event in the first round on Sunday, emerged a winner as he played on the idyllic centre court for the first time.
Nadal has a vast number of ranking points to defend on clay after lifting titles in a spectacular 2018 run at Monte Carlo, Barcelona, Rome and Roland Garros.
The 26-year-old who played the 2018 French Open final against Rafael Nadal and won the Indian Wells Masters title on hardcourt a month ago for a career breakthrough, explained the parting of ways.