Draper had been the final Briton standing within the singles after Cameron Norrie and Dan Evans misplaced on Monday.
He was the higher of the 2 within the second set, benefiting from an more and more faltering opponent to interrupt to like for a 3-2 lead, and closed the set on a wild Hurkacz forehand.
The refocused Pole, who gained his first clay-court title on the Estoril Open on Saturday, broke rapidly within the third however couldn’t serve out the match on the first try as Draper upped his return sport.
Nevertheless, Hurkacz was the stronger within the ensuing tie-break to arrange a gathering with Spain’s Roberto Bautista Agut.
Earlier, third seed Carlos Alcaraz withdrew from the event with a muscle damage in his proper forearm.
The Wimbledon champion had been on account of play Canada’s Felix Auger-Aliassime on Wednesday and practiced in Monte Carlo along with his forearm taped.
Alcaraz is the defending champion on the Barcelona Open, which begins on 13 April.