Ronaldo received a player-of-the-month award before kick-off and continued his good recent form with the opening goal, becoming the first player to score 400 goals in Europe's top-five leagues in the process.
The Argentine moved to Milan on loan in August after two seasons at Juventus, where he won two Serie A and Coppa Italia titles. Daniel Bessa equalized in the second half to make it 1-1.More news: Mayweather Shades Canelo's $365M Deal: I Can Make That in 36 Minutes
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Tahith Chong trained with Manchester United's first team ahead of their Champions League clash with Juventus as a replacement for Alexis Sanchez.
Genoa had to wait until the 53rd minute for their first attempt on target but Juve keeper Wojciech Szczesny tipped Krzysztof Piatek's shot around the post.
Ronaldo eventually got a first win over a Mourinho team in a Premier League outing at Old Trafford in November 2005, playing the full game and setting up Darren Fletcher's victor to end Chelsea's 40-match unbeaten league run.
He has not started a game for United since failing to impress during the club's last Champions League game - a poor 0-0 draw with Valencia at home. Earlier, Roma suffered a 2-0 defeat at home to SPAL courtesy of an Andrea Petagna penalty and a Kevin Bonifazi header either side of the break.