Thirty-six-year-old Paolini used all his guile and experience to attack on a fast descent seven kilometres from the finish to take a first career stage victory in what is, incredibly, a maiden appearance in his home tour.
Winner of the Omloop Het Nieuwsblad semi-classic race in February, Paolini's only previous Grand Tour stage victory came in the 2006 Vuelta a Espana.
"It's incredible to win like that and take the pink jersey as well," he said. "My father was in hospital today for a minor operation and so this pink jersey is for him."
"I suffered to stay on during the climb and tried to ride at my pace. I knew there was a little climb near the finish and know I can descend pretty well. I went for it. I rode as if it was a Classic. We had a good TTT and so I knew I could take pink if I won. I did it."
Britain's Bradley Wiggins also finished safely in the chasing pack and is now second in the general classification, 17 seconds behind Paolini. But team-mate Salvatore Puccio, the overnight race leader, was dropped on the second of two climbs towards the finish of the 222km stage from Sorrento and so surrendered the maglia rosa to his elder countryman.
Italian race favourite Vincenzo Nibali of Astana sits in fifth position on GC, 31 seconds behind Paolini, while Hesjedal - who put in several digs on the final climb - is seventh, a further three seconds back.
Michele Scarponi (Lampre-Merida) saw his chances for a high overall finish dented after the Italian suffered a crash close to the finish of the long 222km stage from Sorrento.
Instigated by Italian Manuele Boaro (Saxo Bank-Tinkoff), a group of seven riders attacked from the outset to build up a maximum lead of seven minutes as the race headed south along the picturesque Amalfi Coast.
Fabio Taborre (Vini Fantini), Willem Wauters (Vacansoleil-DCM), Jarlison Pantano (Colombia), Bert De Backer (Argos Shimano), Dirk Bellemakers (Lotto Belisol), Jackson Rodriguez (Androni Giocattoli) and Boaro reached the foot of the first major test of the day - the Cat.3 San Mauro Cilento - with a lead of 6:50 over the pack.
Belgian youngster Wauters took maximum points over the summit, 68km from the finish, to secure the blue king of the mountains jersey.
Meanwhile, pure sprinters such as stage one winner Mark Cavendish (Omega Pharma-Quick Step) and French national champion Nacer Bouhanni (FDJ) had been dropped off the back of the peloton.
Team Sky led the peloton over the summit 3:42 down on the six leaders, who had dropped Belgium's De Backer on the opening section of steep hairpin bends.
In a sudden rush of blood to the head, Taborre - just 22 seconds down off the race summit after Vini Fantini's fifth place ride in Sunday's team time trial on the island of Ischia - attacked his fellow escapees on the undulating drag ahead of the final climb.
Dreaming of both the stage victory and the pink jersey, 27-year-old Taborre soon held a one-minute gap over the chasing quintet and 3:30 over the peloton.
But there were still 40km left to ride and once Garmin, Sky and Astana combined to drive the pace on the front of the peloton, Taborre's lead came tumbling down.
First the remnants of the break were swept up then, with 25km remaining, an exhausted Taborre was caught at the same moment Hesjedal put in a surprise attack from the main pack.
The Canadian opened up a small gap over his rivals on the Cat.3 Sella di Catona before easing up to nestle back inside the group containing all the race favourites. But now the 23-year-old Puccio had called it a day, opening the door for a new race leader.
With the group staying together over the summit, that new race leader looked all but certain to be his team-mate Wiggins - until Paolini, the unlikely Giro debutant, made his move on the crash-strewn descent.
While the likes of Carlos Betancur (Ag2R-La Mondiale), Tanel Kangert (Astana) and Emanuele Sella (Androni Giocattoli) were amongst the many falls, Paolini kept his cool on the highly technical descent back towards the Mediterranean coast.
Blanco pair Robert Gesink and Steven Kruijswijk led the chase - but both riders overshot a tight bend and tumbled in a heap. In the melee, Scarponi also came a cropper and crashed heavily onto his shoulder.
Gesink remounted quickly and Kruijswijk soon followed. But Scarponi's bike was broken and the 2011 Giro d'Italia champion was forced to wait for a replacement.
Paolini ploughed on and had the luxury of being able to sit up and savour the finishing straight before crossing the line - safe in the knowledge that the bonus seconds would propel him to the pink jersey.
As for Scarponi, the 33-year-old came home one minute down - and so lost 44 seconds to his rivals on GC. But spare a thought for another Italian veteran, Astana's Paolo Tiralongo, who finished the stage in last position 20 minutes in arrears after crashing in the feed zone.
The Giro d'Italia continues on Tuesday with the 246km stage four - which, with two decisive climbs tagged on the end, is an almost carbon copy of Monday's stage.
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- Michele Scarponi