The Rossoneri were made to work hard for last week's 1-0 win over Sampdoria but proved far too strong for Genoa as they put on a show for their returning supporters, scoring all four goals in the first half.
Alessandro Deiola netted Genoa's first goal in six league games versus Milan to cancel out Sandro Tonali's opener, but Rafael Leao's heavily deflected strike and Giroud's double gave the hosts breathing space at the midway point.
Milan was happy to keep hold of possession from that point on as it cruised to a seventh league game without defeat stretching into last season.
Tonali lifted the ball over the Genoa wall and just out of back-up goalkeeper Boris Radunovic's reach to get Milan up and running inside 12 minutes with just his second Serie A goal.
Stefano Pioli's side were pegged back soon after through a Deiola header after the midfielder was picked out by a smart Joao Pedro pass – the first goal Milan had conceded in seven league matches.
But Leao restored his side's advantage in rather fortuitous circumstances as his shot took a big touch off the back of Brahim Diaz – Milan's match-winner last weekend – and flew past Radunovic.
Giroud's first Milan goal followed seven minutes later, the Frenchman curling a first-time shot into the far-left corner when played in by Diaz, and he had a second before half-time when converting a penalty awarded for a Kevin Strootman handball.
Milan then went through the motions and did not register a single attempt on target in the second period, with Charalampos Lykogiannis going closest to scoring for the visitor when testing Mike Maignan 10 minutes from time.