This was the 33-year-old's 400th career goal in Europe's top five leagues, making him the first player to reach that tally.
Andreas Pereira has said that Manchester United's performance against Chelsea in the Premier League on Saturday has left them feeling "pumped up" for the upcoming Champions League clash with Juventus.
"We have to take the positives from the game and I think the way we played in the second half especially, we were fantastic at times".
Lionel Messi is next best on 389.
Genoa had to wait until the 53rd minute for their first shot on target, and unsurprisingly it fell to Piatek, but his hopes of swelling his nine-goal Serie A haul were dashed when Juve keeper Wojciech Szczesny tipped his shot around the post.
At one stage, Ronaldo looked to be in danger of missing the game entirely after he was shown a red card in Juve's Champions League opener against Valencia for pulling Jeison Murillo's hair, but in the end he was only given a one-match ban.
It took almost four years for Ronaldo to get his next win - in 90 minutes - over a Mourinho team, as his Inter visited Old Trafford in the Champions League and lost 2-0 in March 2009.
Juve are now four points clear on top of the table ahead of second-placed Napoli.
There were further chances for Ronaldo, Miralem Pjanic and substitute Paulo Dybala but Genoa stood firm to earn an unexpected point. 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. Every match has to be won on the pitch in 90 minutes.