Jonathan headed Inter ahead, Rodrigo Palacio scored twice, including one penalty and Andrea Ranocchia completed the rout in the third qualifying round tie against the Serie B team.
Italy's big guns usually sit out the early stages of the competition as the top eight teams in Serie A enter the fray in the round of 16 the following season.
Inter, however, paid the price for their dismal end to last season when they finished ninth.
Jonathan headed Inter in front from a Fredy Guarin cross in the 17th minute and Argentine forward Palacio converted a penalty after half an hour after he was fouled by Simone Pecorini, who was sent off.
In front of a San Siro stadium which was barely one quarter full, the other goals came in the second half as Palacio ran onto another Guarin pass and Ranocchia scored following a corner.
Mazzarri joined Inter after four seasons at Napoli, where he built a strong attacking side which twice qualified for the Champions League and winning the Italian Cup in 2012.
Andrea Stramaccioni was fired by Inter after last season's campaign, even though club president Massimo Moratti had repeatedly said he was not at fault after his side were decimated by injuries.