Goals in each half from loanee Adel Taarabt and Keisuke Honda saw Milan claim a hard-fought win and close within five points of rivals Inter – who sit fifth and occupy Serie A's final European place.
They suffered a nervy finish though, with Genoa defender Marco Motta's excellent 20-yard strike coming with 17 minutes to play.
The France defender got back to nod Motta's header off the line and away to safety as Milan's good run continued.
Milan, who dropped top scorer Mario Balotelli to the bench, started brighter, with Taarabt's cross just evading the onrushing Kaka in the ninth minute.
Two successive wins looked to have restored Milan's confidence, and although they did not have a shot on goal until the 20th minute, their first effort was successful.
Genoa continued to press after the interval, as Milan goalkeeper Christian Abbiati kept out Ioannis Fetfatzidis before Giovanni Marchese headed over the bar.
Milan's second goal came against the run of play, as Honda scored for the first time in the league for the Italian giants.
Taarabt's ball played Honda through and he cleverly dinked over Perin, only to see Giuseppe Sculli tracking back and closing in on the ball.
Genoa – who have posted seven of their 10 league wins this season at home – gave themselves hope when Motta hooked in a brilliant finish from distance following a corner.
But despite Genoa's late pressure, Milan's desperate defence helped them continue their winning run – and their faint European hopes.
