The Brazilian scored a looping header in first half stoppage time before adding to his tally with a wonderful effort inside the box to move Milan back into second place.
Zlatan Ibrahimovic had given the Rossoneri an early lead with a magnificent curling freekick as Milan were in complete control at the Stadio Luigi Ferraris.
Maignan 7; Kalulu 6.5, Kjaer N/A (‘4 Gabbia 6 (’46 Florenzi 6)), Tomori 7, Theo Hernandez 6.5; Tonali 6 (’77 Saelemaekers N/A), Kessie 6; Messias 8, Diaz 7.5 (’77 Bakayoko N/A), Krunic 6.5; Ibrahimovic 7.5 (’60 Pellegri 6)
Player of the match: Junior Messias
After making such a memorable impact in the Champions League against Atletico Madrid last week, Messias was at it again with a well-taken brace to kill off any hopes of a Genoa fightback. A deft header was followed up by a bending effort that Grifone coach Andriy Shevchenko would have been proud of in his Milan pomp.