Having made a flying start to their campaign, Milan's loss to champions Juventus preceded two surprise draws on the road against Empoli and Cesena.
However, Filippo Inzaghi's side got back to winning ways on Saturday with a hard-fought victory over Chievo courtesy of Muntari's second-half volley and a well-struck Honda free-kick.
After a first half of few chances, it took Milan just 10 minutes of the second period to move ahead - with Muntari scoring his second goal of the campaign.
The Ghana international struck a volleyed effort from distance into the ground, which looped up and over helpless Chievo goalkeeper Francesco Bardi to end the resistance of the visiting defence.
Eugenio Corini, whose side are without a win since beating Napoli in mid-September, saw any hopes of a draw ended when Japan international Honda fired home 12 minutes from time.
Honda's fourth goal from just six games extended Milan's unbeaten run against the Verona club to 16 contests, while the defence held on for a first clean sheet under former striker Inzaghi.
Jeremy Menez started despite fears over a knee injury and was the hosts main attacking outlet, firing wide from the edge of the area early on before Maxi Lopez saw appeals for a penalty waved away when he tangled with Alex in the hosts' area.
Fernando Torres was next to go close, with the Chelsea loanee's effort diverted marginally off target by team-mate Giacomo Bonaventura after 17 minutes.
However, in a game littered with fouls early on, chances were few and far between in a scrappy affair.
Milan had a penalty shout turned down when Menez's cross kicked up off Isaac Cofie's boot and appeared to hit the Ghanaian on the hand.
The hosts' best chances came following a quick corner that saw Menez thwarted by Bardi before Torres blazed wide following a goalmouth scramble.
And Menez continued to prove Milan's source of inspiration after the interval, whipping in a dangerous delivery that Honda failed to connect with.
However, the hosts' pressure paid off 10 minutes after the break when Muntari hit a volley from distance and saw his strike into the ground loop over Bardi and in.
Honda again wasted a golden opportunity soon after when he failed to connect with Ignazio Abate's cushioned delivery before Muntari almost undid his good work as he lost possession cheaply to Dejan Lazarevic.
The substitute misplaced the final ball, letting Milan off the hook when Chievo had been three on one.
With Chievo having wasted their best chance to leave San Siro with a point, Honda put the game beyond them with a dipping free-kick that Bardi failed to keep out.
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