Knowing that Spain's midfielders were unstoppable when they had the ball, Italy bypassed the middle of the park - either through high/long balls from defence or through long on-the-ground veritical passes into the Spanish defensive third.
This had 2 effects. One, it removed the Spanish attacking quarter of Iniesta, Fabregas, Nolito & Silva from the game. Two, it put immediate pressure and confusion on the Spanish defensive trio of Busquets, Pique and Ramos. That combined with the Spanish fullbacks often higher up the pitch meant that Spain were always on the back foot with little time to gather themselves and find their footing. Jordi Alba and Juanfran were never around to give enough support to the defence. The net effect was to allow Italy's 5 man midfield to overload the Spanish defensive zone.
Finally, Graziano Pelle was the perfect striker against Pique and Ramos, both of whom are not very good with high balls and against strong opponents. Instead of trying to be the point man for Italy's attacks, Pelle came back just a little bit for the two Spanish central defenders to open up spaces for the Italian midfielders to move into. Pelle was often laying up balls and assisting the flow of the movements. That helped Italy be more fluid, which is often not the case with a 3-5-2 formation.
Next Italy face my favourite team, Germany. It will be interesting to see Conte's tactical plan to counter the Germans.