The attacking midfielder netted a brace at the Stadio Marc'Antonio Bentegodi to seal back-to-back wins for Filippo Inzaghi's side following victory over the hosts' city rivals Chievo before the international break.
With the two teams heading into the game level on 11 points, a visit to Verona was viewed as a stern test of Milan's recent revival under Inzaghi.
But the 18-time Italian champions were given early assistance as a spectacular own goal from Brazilian defender Rafael Marques put them ahead.
Honda then doubled that lead in the 27th minute and made the game safe in the second half to take his tally for the season to six in seven matches.
Milan could not keep a clean sheet as forward Nico Lopez pulled one back for Verona late on, while defender Rafael Marquez saw red for a second bookable offence.
The triumph furthers Milan's UEFA Champions League credentials, which will be challenged again next week when they welcome Fiorentina to San Siro.
Milan fashioned the first real chance of the game after 13 minutes as Fernando Torres turned sharply in the area and shot narrowly wide of the near post.
Verona appeared solid at the back in the early stages but conceded the initiative in unconventional fashion in the 21st minute when Marques volleyed Ignazio Abate's right-wing cross into his own net.
The hosts went close to responding through Iceland midfielder Emil Halfredsson, only to be punished on the counter by Honda soon after.
Japan playmaker Honda cruised into the box to latch on to Stephan El Shaarawy's pass and steer a cool finish into Rafael's bottom right-hand corner.
Andrea Mandorlini's Verona did carry a threat going forward, though, Luca Toni's spectacular overhead kick kept out by Christian Abbiati, who then denied Bosko Jankovic with a superb flying save down to his right.
Inzaghi's men looked to sit back and frustrate Verona in the second half and their task of seeing out the game was made easier in the 56th minute when Honda raced on to Adil Rami's long ball over the top to slot home Milan's third.
Despite the heavy deficit, Verona refused to lie down, but they were unfortunate to find Milan goalkeeper Abbiati in stunning form, Panagiotis Tachtsidis thwarted by the 37-year-old veteran as his powerful drive was tipped over the crossbar.
Lopez added a consolation three minutes from time before Verona were reduced to 10 when Marquez felled Giacomo Bonaventura.
However, that proved immaterial, with Milan's fine performance at both ends of the field boosting hopes that Inzaghi - who won two Serie A titles and Champions League crowns in 11 years as a player with the club - can return them to their former glory.
