Luxembourg's Frank Schleck was third and Ryder Hesjedal, finishing fifth, became the first Canadian to wear the overall leader's pink jersey after overnight leader Adriano Malori of Italy was dropped with 15 kilometres to go.
Tiralongo is second overall, 15 seconds back and Spain's Joaquim Rodriguez third.
Astana rider Tiralongo shot past 2011 Giro winner Scarponi to claim the win as a 50-strong front group of favourites shattered on the shallow but relentlessly rising 19-km climb.
"I shadowed Michele for as long as I dared before making my move," Tiralongo, winner at the Macugnaga summit finish in last year's Giro, told reporters.
"With about 50 metres to go I told myself it was now or never."
The 34-year-old was so exhausted after his last-ditch effort that he lay prostrate on the ground for almost half a minute before race officials helped him to his feet.
"I had to go in very deep but a Giro stage is always worth it," Tiralongo added.
Former mountain bike rider Hesjedal overcame his disappointment in missing out on the race lead on Friday to add to the Garmin-Barracuda squad's spectacular start to the Giro, despite losing sprinter Tyler Farrar through a crash.
"I was only 17 seconds away from getting the lead yesterday and it was very frustrating, I was upset," Hesjedal, a former team mate of seven times Tour winner Lance Armstrong, said. "But today it worked out well."
"The team told me to stay confident and were behind me 100 percent, and (team mate) Christian Vande Velde put me in perfect position for the final part of the climb."
After winning the team time trial and leading the race for two days through Lithuanian Ramunas Navardauskas, the squad have regained the overall classification, are top of the team competition and lead the young riders category with American Peter Stetina.
"The team's been incredible and I hope to try to live off that momentum as long as possible," said Hesjedal whose previous big success was a stage in the 2009 Vuelta a Espana.
"I have no idea how long I'll lead the race. Yesterday we thought we would get it and it was a big opportunity wasted. Today we did get it, so I'm going to take it day by day.
"But I am usually strongest in the third week of Grand Tours, and that's when you can lose or gain a lot," he added.
Sunday's 229-km stage through the mountains of southern Italy from Sulmona to Lago Laceno should provide more answers about the overall contenders.
The Giro d'Italia finishes in Milan on May 27.
1-Paolo Tiralongo (Astana) in 5:51:03 average 35,379 km/h
2-Michele Scarponi (Lampre ISD) s.t.
3-Frank Schelck (Radioshack Nissan) at 3 secs
1-Ryder Hesjedal (Garmin Barracuda)
2-Paolo Tiralongo (Astana) at 15 secs
3-Joaquin Rodriguez (Katusha) at 17 secs