Federico Bernardeschi had given the Azzurri the upper hand inside two minutes but it took Italy until midway through the second half to score again through Belotti, with Alessio Romagnoli and Stephan El Shaarawy boosting the visitors clear before the Torino man rubbed salt in Liechtenstein's wounds.
Salanovic and Maximilian Goppel issued an early warning to Italy that Liechtenstein – 182nd in the FIFA rankings – were not ready to roll over as both players went close to beating Salvatore Sirigu in the first minute.
However, Bernardeschi would remind the principality team of their lowly status by firing the Azzurri into an early lead.
Raiding forward rapidly following Goppel's near miss, left-back Cristiano Biraghi played a one-two to get free down the left wing before playing a cross inside for Bernardeschi to smash home the opener.
Liechtenstein were not cowed and shortly after the restart Sirigu denied Salanovic once again.
Despite dominating the space, Italy could not carve out another opening before the break and they were lucky to preserve their lead heading into half-time as Salanovic almost equalised, Sirigu reacting quickly to push his long-range drive behind for a corner.
Italy returned to the field focused on turning up the pressure in pursuit of a second goal and Zaniolo went close to grabbing it in the 54th minute.
Bryan Cristante was next to threaten, with Inter Milan's Biraghi then trying his luck from distance.
Still the potential for a Liechtenstein goal loomed over Italy and after the hour mark Sirigu had to keep FC Thun winger Salanovic out once again.
Those lingering fears finally faded when, in the 70th minute, Belotti made it two with a firm header from Vincenzo Grifo's corner.
Suddenly Italy were off the leash and it took them only seven minutes to reach 3-0, Romagnoli connecting with El Shaarawy's short cross to nod the ball past Buchel.
Provider turned scorer five minutes later as Shanghai Shenhua star El Shaarawy buried Cristante's through ball beyond an increasingly hapless Buchel.
Liechtenstein's brave endeavours were forgotten by the time Belotti bagged his brace deep into stoppage time, the Toro hitman piercing Buchel's barricade one last time from a Giovanni Di Lorenzo assist.