Urby Emanuelson opened the scoring in the 16th minute, although the lead lasted only two minutes before Sergio Pellissier levelled.
Riccardo Montolivo and Bojan Krkic gave Milan a comfortable half-time lead before their top goalscorer Stephan El Shaarawy got his customary goal in the 75th minute.
Giampaolo Pazzini added a fifth to wrap up victory with the last kick of the game.
Milan struck first after a tight opening quarter of an hour, with Emanuelson hitting a first-time volley into the far corner after Boukary Drame misjudged a long ball forward.
Two minutes later, a corner from the left was met at the near post by Pellissier, who nodded the ball inside Christian Abbiati's near post.
Chievo had the chance to go ahead in the 35th minute when Cyril Thereau's cross was pushed wide by an unsighted Abbiati.
Milan responded to that scare with Montolivo's shot from distance taking a slight deflection on its way into the bottom left-hand corner of Stefano Sorrentino's goal in the 37th minute.
Four minutes later Bojan netted his first goal in Serie A, with another deflected shot wrong-footing Sorrentino.
Drame was forced to leave the field soon after the break when Ignazio Abate's cross struck him on the head and Chievo's hopes of recovering hit the deck with the Senegalese defender.
El Shaarawy placed a shot wide from 15 yards in the 70th minute before getting his name on the scoresheet as if by habit five minutes later.
Another cross from the right from Abate was met by the Italy international, who was alone at the far post to accept the gift for his eighth goal of the season.
Milan were not satisfied with only four goals, though, and a good counter-attack involving Kevin Constant and Pazzini presented Krkic with a good chance, but he shot straight at Sorrentino.
Pazzini then got on the end of El Shaarawy's cross to round off the victory deep into stoppage time.