The eight-time winner beat Verdasco 6-4 6-4 one day after racing through two matches in which he dropped just two games.
Nadal faces Tsitsipas on Saturday, one week after the latter was victorious in their semi-final meeting in Madrid.
Tsitsipas was handed a walkover in Rome after Roger Federer withdrew before their quarter-final.
Federer pulled out due to an injury in his right leg, with the Swiss 37-year-old having played five sets on Thursday after beating both Joao Sousa and Borna Coric.
Earlier on Friday, Diego Schwartzman overcame Kei Nishikori 6-4 6-2 to reach the last four.
Schwartzman will face the victor of Novak Djokovic vs Juan Martin del Potro, with the pair in action later this evening.