Milan have hit a strong run of recent form to put themselves in the picture for a top-three finish, and Bacca got them off to the ideal start by firing in the fifth minute after neat work from Honda.
Sinisa Mihajlovic's side were in control throughout, and made sure of the points shortly after the hour, courtesy of a superb long-range strike from Honda.
Genoa failed to really cause Milan any problems, although former Milan loanee Alessio Cerci did grab an injury-time consolation.
Milan could have added a third through Giacomo Bonaventura or Riccardo Montolivo, but will be more than happy with an assured performance that makes it seven Serie A games undefeated.
The hosts sit just four points adrift of third-placed Roma, while Genoa remain three points above the drop zone.
Honda nearly gave Milan the lead after just four minutes with a stunning long-range strike that seemed destined to find the top corner, but Mattia Perin pulled off an excellent save.
Yet the hosts scored just 60 seconds later when Bacca notched his 13th league goal of the season, M'Baye Niang flicked on Honda's cross, and the Colombian finished well beyond Perin.
Bonaventura got on the end of Mattia De Sciglio's cross midway through the half, but his header lacked the power and accuracy to worry Perin.
Bacca could have doubled Milan's lead at the half-hour mark after a clever throughball from Luca Antonelli, but Perin did well to rush off his line and make a vital interception.
Former Milan forward Suso got a chance to level the scoring after a quick Genoa counter-attack, but he hesitated just too long and eventually saw his shot deflect wide off Alessio Romagnoli.
Mihajlovic's men caused Genoa plenty of problems from set-pieces and Romagnoli nearly made it two after a corner from Bonaventura, only to place his header just wide.
But Honda eventually doubled Milan's lead in the 64th minute, as the 29-year-old unleashed a powerful low shot from 25 yards out that left Perin without a chance.
Montolivo then rattled the upright as Milan searched for more goals, before Jeremy Menez made his long-awaited return from injury off the bench.
Cerci marked his return to San Siro with a late consolation for Genoa, but Milan's resurgence continues.