Zlatan Ibrahimovic won and converted a second-half penalty and Antonio Nocerino side-footed the second while the hosts had former Milan defender Kakha Kaladze sent off in the 54th minute.
In between the goals Robinho somehow contrived to scoop the ball over the bar from two metres after a low cross by Alberto Aquilani who was left thumping the ground in anger.
"Robinho also played an important part in the penalty, football is like that," said Milan coach Massimiliano Allegri. "We controlled the match after the first goal."
Ninth-placed Genoa's defeat adds to the pressure on Alberto Malesani, the favourite to become the next Serie A coaching victim.
Milan have 27 points from 13 games.
The game was halted for nine minutes in the first half after the teargas incident left players, officials and fans coughing and wiping their eyes.
Local media said police threw the teargas to stop scuffling outside the stadium.
NOCERINO DENIED
Nocerino was twice denied early on, by a last-gasp Marco Rossi tackle and then by goalkeeper Sebastien Frey.
Milan continued to dominate when play restarted following the interruption, Kevin-Prince Boateng hitting the side netting, Nocerino going close again and Frey parrying an Ibrahimovic effort.
Genoa then came to life with Miguel Veloso's dipping free-kick tipped over by Marco Amelia and Giandomenico Mesto firing across the face of the goal following sloppy Milan defending.
The visitors broke through in the 56th minute when Ibrahimovic cleverly flicked the ball past Kaladze and was scythed down by the Georgian who earned a second yellow card.
The Swede fired the resulting penalty into the roof of the net.
Aquilani then won possession before turning and crossing for Robinho who made his second remarkable miss in 10 days, following another dreadful effort against Barcelona.
Nocerino made no mistake from a similar distance after Boateng weaved his way to the byline and crossed to the midfielder in the 79th minute.
