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.
Ronaldo's fifth Serie A goal for Juve was added to his 84 Premier League strikes for Manchester United and 311 in La Liga for Real Madrid. Daniel Bessa equalized in the second half to make it 1-1.
A communications mix-up saw Piatek leave Joao Cancelo's blocked shot for his keeper, but the loose ball fell at Ronaldo's feet and he tapped in to an empty net.
Alexis Sanchez unexpectedly missed Manchester United's final training session before their Champions League clash with Juventus.
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Juve paid heavily for failing to kill off the encounter when Bessa headed a cross from Christian Kouame into the back of the net on 67 minutes.
Napoli cut the gap on Juventus to four points with a third successive win in all competitions and a third clean sheet in a row after a 3-0 win at Udinese.
Allegri introduced Paulo Dybala off the bench and both he and Miralem Pjanic fired narrowly wide from distance, but Genoa withstood the late pressure to move 10th in the table and give Napoli the chance to close the gap to the leaders.
Meanwhile, Roma's troubles grew with a 2-0 home defeat by lowly SPAL, who finished the game with 10 men but looked comfortable all the same.
The Curacao-born 18-year-old is considered, alongside Angel Gomes, to be United's most exciting academy product and he impressed on the club's tour to the United States last summer. Every match has to be won on the pitch in 90 minutes.