Filippo Inzaghi's side made an impressive start to the league campaign, taking maximum points from their first two fixtures.
However, following a narrow defeat to champions Juventus, Milan were then held to frustrating draws by Empoli and Cesena last month.
Following a drab opening period, second-half goals from Sulley Muntari and Keisuke Honda settled the game and brought an end to the home side's mini-slump.
Muntari struck a volley from distance into the ground that dipped over Fracesco Bardi before Honda put the game beyond Chievo with a well-struck 78th-minute free-kick.
The Japan international now has four goals to his name from six Serie A appearances this term while Milan's clean sheet was the first of former striker Inzaghi's tenure.
Chievo's city rivals Hellas Verona were on the right end of a 1-0 scoreline against Cagliari, as the visitors' poor start to the campaign continued.
Zdenek Zeman's men caused a stir with a 4-1 win over Inter at San Siro last weekend but were unable to build on the victory as they fell to a late Panagiotis Tachtsidis goal.
Bosko Jankovic and Luca Toni both hit the woodwork for the home side before Tachtsidis scored the winner a minute from time to continue the hosts' strong start to the campaign.
Verona now sit sixth in the top flight, having bounced back from their defeat to Roma last weekend - their only loss in Serie A so far
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