Italy were not immediately switched on; however, once they were, they were dominant.
Spalletti's men pressed energetically, overturning possession to create chances to possibly inflict further damage.
Winger Chiesa was particularly impressive, dribbling forward with ease despite the number of Albania shirts around the box.
Italy were well drilled and passed intelligently to try to pull Albania's defence out of shape, although striker Scamacca did little to impress in the box when the ball was worked his way.
Their attacking intent ultimately fizzled out, but victory never looked in much doubt.
Italy are a team in transition, with a new manager and a markedly different squad from Roberto Mancini's group who beat England on penalties in the final of the last Euros.
Difficult group games against Croatia and Spain remain as they look to step up their trophy defence, but Saturday's victory - setting aside that dreadful early blip - was a strong showing to kick off their campaign.