Andrea Mandorlini, a lifelong Inter fan and veteran of nearly 200 games in the Nerazzurro shirt, had coached his promoted Verona side into fourth place with five wins from eight top-flight games.
But Inter are enjoying their own resurgence under Walter Mazzarri following last season's dismal ninth-placed finish and his team built an early lead through Vangelis Moras' own goal and a sixth goal of the season from Rodrigo Palacio.
Raphael Martino's classy response was quickly trumped by a third Inter goal from Esteban Cambiasso but, after Porto loanee Rolando put the result beyond doubt with his first goal for the Italians, Romulo made the scoreline respectable for the visitors with a precise late contribution.
Sampdoria moved away from the relegation zone with a hard-fought 1-0 win over 10-man Atalanta.
Shkodran Mustafi scored the only goal of the game in the 56th minute for the Blucerchiati, who made their fans suffer on the way to their first home win - and only second overall - of the season.
Atalanta finished the game with 10 men after Constantin Nica was sent off in the 63rd minute, although they still caused the home team several problems as the clock ran down.