Italian Gatto darted away on a short, sharp climb just before the finish in the coastal town of Tropea, with three-times Tour de France winner Contador in hot pursuit.
The two crossed the line with a five-second advantage over the pack, led in by stage two winner Alessandro Petacchi of Italy.
After moving up to fifth overall, Contador was upbeat.
"I was in the front of the bunch and I decided to try my luck," the Saxo Bank rider told reporters.
"I felt good and it was a good opportunity to get a few seconds advantage, so I took it." Gatto said he couldn't believe his eyes when he saw the Spaniard chasing him down.
"I looked back once and didn't see anybody, then a second time saw a Saxo Bank jersey and thought 'that can't be him," Gatto told reporters.
"It was hard to find the right moment to attack, it looked like it was going to be a bunch sprint until that final little climb. I couldn't win by much but it's winning that matters." "After seeing what Alberto did today, I'm sure he'll be very strong tomorrow," added Gatto.
Dutchmam Pieter Weening retained the overall lead for a fourth successive day and was optimistic about his chances on Sunday on Mount Etna.
"Today was pretty easy, only the last part was technical and dangerous and you had to be sure you stayed near the front," Weening told reporters.
"I'll give it everything tomorrow to hold onto the lead." A special ceremony was held by the Giro d'Italia organization during the stage at the site of a crash last December where eight cyclists from the town of Lamezia Terme were killed in a collision with a vehicle.
Giro officials unveiled a plaque in honor of the victims shortly before the race passed through.
The Giro d'Italia finishes in Milan on May 29.