Cristiano Ronaldo gave Juventus a deserved lead in a dominant first half, but sloppy defending from the hosts allowed Daniel Bessa to draw Genoa level after the break and end Juve's winning streak at ten matches in all competitions.
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.
Since 2003, Ronaldo has tallied 311 goals for Real Madrid, 84 goals for Manchester United, and five goals for Juventus.
Ronaldo, who returns to Old Trafford on Tuesday to face his old club Manchester United, would have bagged a double shortly after but his low shot was denied by Genoa keeper Ionut Radu's diving save.
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Krzysztof Piatek, who has been in fine form this season, almost equalised with a long-range shot in the 55th minute but Wojciech Szczesny kept it out.
"It will be a great Champions League night, United are strong, and like us they will also try to win".
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.
Juve are now four points clear on top of the table ahead of second-placed Napoli. Every match has to be won on the pitch in 90 minutes. There were further chances for Ronaldo, Miralem Pjanic and substitute Paulo Dybala but Juric's players stood firm to earn an unexpected point.