Vittozzi shot clean under enormous pressure to win by a margin of 28.8 seconds over Norway's Maren Kirkeeide, who stormed back from two late misses to secure silver.
Suvi Minkkinen of Finland took bronze.
The start order in the pursuit was decided by the finishing times of the sprint, meaning Kirkeeide set off first, with Vittozzi going 40.6 seconds after.
Consisting of five 2km laps and four visits to the shooting range, the race took place in bright sunshine with a light wind that occasionally made aiming difficult, and each miss meant a trip around the 150-metre penalty loop.
The ding-dong battle began on the second shoot as Kirkeeide missed. But so too did Lou Jeanmonnot of France, who had been making the early running with the Norwegian, and Vittozzi hit her five shots in quick succession to take the lead.
However, the Italian was quickly reeled back in by Kirkeeide, who came into the third shoot in the lead, and the race was soon between the Norwegian and Vittozzi as Jeanmonnot missed twice to drop out of medal contention.
Final twist in the tale
Vittozzi again hit all five targets to keep up with Kirkeeide after the third shoot, and it looked like the Norwegian's greater skiing power might see her through.
However, there was one more twist in the tale. As it all came down to the last shoot, Kirkeeide finally cracked with two costly misses, and Vittozzi, shooting beside her, rattled off a perfect trademark quick-fire series to ski out and secure the gold.
"I'm so happy. What I've done today, I'm really proud of myself. I had goosebumps in the last few kilometres. It was a dream come true," a delighted Vittozzi told Italian TV.
"I didn't think today that I would reach the gold medal because the level of the women is really high, but I really did a good job at the range, and I'm very happy. I was very calm, I tried to work well, and I hit all the targets, so I'm very happy."
Condemned to two penalty loops and out of contention for the gold, Kirkeeide skied frenetically to get back to third, and a heroic effort on the final lap saw her pass Minkkinen to take the silver medal, leaving the Finn to be content with third place.