Ghana striker Boakye struck a quick-fire first-half brace to hand the Serie A side their first win in seven matches and put them through to the final stages of the competition.
In the early evening kick-off, high-flying Genoa’s eight-match unbeaten run came to an end as they suffered a 2-0 defeat to Serie A rivals Empoli at Stadio Carlo Castellani.
On-loan Inter Milan midfielder Diego Laxalt handed the hosts the lead early on before Georgia international Levan Mchedlidze made the game safe deep into the second half to stretch their unbeaten run to four games.
In Wednesday night’s other all-Serie A clash, Udinese and Cesena took their game to extra time at 2-2 after 90 minutes before two goals from the home side saw Andrea Stramaccioni’s men progress.
Milan Duric handed visitors Cesena the lead after four minutes before goals from Allan and Bruno Fernandes turned things around, and Davide Succi netted 10 minutes after the break to take the game to extra time.
The hosts went ahead after 100 minutes through Brazil Under-21 midfielder Lucas Evangelista before Cyril Thereau finished the game off with seven minutes remaining.