The Portugal superstar, 33, reached the tally as he scored in the against Genoa in the 1 - 1 on Saturday.
Massimiliano Allegri's side have won all eight of their opening Serie A matches and are on course to make it nine out of nine if they beat Genoa.
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.
Lionel Messi is next best on 389.
Ronaldo's struck in the 17th minute, tapping in from two yards out after Genoa goalkeeper Ionut Radu failed to deal with a corner.More news: Trump hopes to pick United Nations ambassador from five candidates
Energised, the 23-year-old should have levelled seconds later, outjumping Leonardo Bonucci but his header went wide.
Mourinho's players were photographed arriving at Carrington this morning as they prepare for their biggest European game of the season so far. They are four points above second-placed Napoli - who beat Udinese 3-0 later on Saturday.
With the pressure off, Marko Rog then added a third with five minutes to go. 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.
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.
SPAL took the lead from the penalty spot after 38 minutes.
Ronaldo's only outing against Mourinho's United was in the 2017 UEFA Super Cup, featuring for seven minutes as a substitute in Madrid's 2-1 win.