The victory, which came after Milan's best performance by far this season, moves them up to seventh on 14 points, and will relieve the pressure on manager Massimiliano Allegri. Milan, who have never lost to Chievo at the San Siro, took the lead after 16 minutes through Urby Emanuelson.
He met Marco Andreolli's misplaced headed clearance with a stunning left foot half-volley from the edge of the area which whizzed into Stefano Sorrentino's bottom right-hand corner. But Chievo, who had lost 11 games in a row against Milan going into the match, equalised two minutes later when Sergio Pellissier met a corner at the near post and sent a powerful header past Christian Abbiati for his third goal of the season.
Chievo, who had been more than a match for the hosts, fell behind 10 minutes before halftime when the impressive Riccardo Montolivo finished off a smart passing move by firing home a superb shot from nearly 20 metres.
Bojan, who joined Milan from Barcelona at the end of August, extended the home side's lead after 41 minutes with his first Milan goal when his long-range strike was deflected past the despairing Sorrentino by Dario Dainelli.
Milan were now dominant and with 15 minutes left Serie A top scorer Stephan El Shaarawy capitalised on Ignazio Abate's great wing play and cross to tap home his eighth of the season. Giampaolo Pazzini put the icing on the cake in added time when El Shaarawy broke free on the left and laid the ball on a plate for him to tap home and provide the perfect ending to a rare happy evening for Milan this season. Inter Milan will bid to end Serie A leaders Juventus' 49-match unbeaten league record and close the four-point gap on their old rivals when they play the champions in Turin later on Saturday (1945).