The EF Education-Easy Post rider Healy jumped away from the day's breakaway on the first of two ascents of the I Cappucini climb.
Healy went on to bag his third win of the season, after also taking a surprising fourth place in the Liege-Bastogne-Liege Monument classic last month.
On the second ascent of I Cappucini, triple Vuelta champion Primoz Roglic attacked and dropped his main rivals for the title, only for Geraint Thomas and Tao Geoghegan Hart to reel him in further up the road.
Evenepoel, however, failed to sustain the pace and crossed the finish line 14 seconds behind those three, while Norway's Andreas Leknessund finished some 20 seconds further adrift though he retained the overall leader's Maglia Rosa.
Leknessund leads Evenepoel by eight seconds overall with Roglic in third place, 38 seconds off the pace. Geoghegan Hart, the 2020 Giro champion, moved up to sixth 56 seconds behind Leknessund.
Sunday's stage nine is a 35km individual time trial from Savignano sul Rubicone to Cesena.