Paolini, who rides for Katusha, broke away toward the end of the final descent to complete the 222-kilometre leg from Sorrento to Marina di Ascea in five hours 43 minutes 50 seconds.
Cadel Evans beat defending champion Ryder Hesjedal in a bunch sprint for second place, with both finishing 16 seconds behind. Overall favourite Bradley Wiggins finished eighth on the stage and is second in the general standings, 17 seconds behind Paolini. Main rival Vincenzo Nibali is fifth, 14 seconds further back.
Paolini, who is riding in his first Giro d'Italia at the age of 36, timed his break to perfection on the descent of the Sella Di Catona, attacking 6.5 kilometres from the finish.
Hesjedal attacked several times on the second and final classified climb but could not build up enough of an advantage and was caught each time. The Victoria native's third-place finish in Monday's stage moved him into seventh in the overall classification, 34 seconds behind Paolini.
"It's incredible to win like that and take the pink jersey as well," Paolini 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 (one-day) classic."
The third stage took the peleton along the picturesque Amalfi coast, and featured an early breakaway by seven riders who built up a lead of more than seven minutes at the midway point.
But the Sky riders, who won the team trial in the second stage on Sunday, was in control of the peleton and the gap slowly began to shrink as they approached the start of the first climb of the day, up the San Mauro Cilento. At the summit, the leaders had an advantage of just over four minutes.
Fabio Taborre made a solo break away from the leading group with 50 kilometres to go, but the peloton again picked up the pace and swallowed up the chasers before catching the Italian.
Hesjedal then attacked with 25 kilometres remaining, was caught and broke again together with Valerio Agnoli and Paolini.
The group was again back together 14 kilometres from the finish before Paolini's attack on the final part of the twisting descent to the line.
Tuesday's fourth stage is another hilly and lengthy 246-kilometre leg from Policastro Bussentino to Serra San Bruno. It is the second-longest leg of this year's Giro.
The race ends on May 26, in Brescia.