Serie A: Genoa 1 Milan 2
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.
And Genoa were inches away from claiming an equaliser, with Philippe Mexes denying Motta a second goal.
The France defender got back to nod Motta's header off the line and away to safety as Milan's good run continued.
They remain 11th in the table but after a dreadful start to the season, the fact they can still reach Europe will encourage coach Clarence Seedorf.
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.
Taarabt was responsible, charging forward and beating three men at pace before unleashing a vicious 20-yard drive that hit the bottom-left corner and gave Genoa goalkeeper Mattia Perin no chance.
Stefano Sturaro showed quick feet to find space just outside the box, but could only fire wide as Genoa pressed for an equaliser, with Andrea Bertolacci next to go close.
Bertolacci hit a fierce left-footed drive from 25 yards that went agonisingly wide and the same player saw another long-range shot deflect out for a corner as the hosts ramped up the pressure.
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.
Sculli should have kept the ball out but could only help it over the line with a despairing effort, giving Milan much-needed breathing space.
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.
And Genoa could have drawn level just one minute later, when Sturaro drew a fine reaction save from Abbiati before Mexes kept out Motta.
But despite Genoa's late pressure, Milan's desperate defence helped them continue their winning run – and their faint European hopes.