Ronaldo, 31, fired Madrid ahead with his 367th goal in one of Europe’s top-five leagues, eclipsing the mark set by former England striker Greaves in 1971.
Ronaldo slotted in a second and, after John Guidetti gave 10-man Celta hope, Karim Benzema and Toni Kroos sealed it.
Real will clinch La Liga with a draw at mid-table Malaga on Sunday.
Rivals Barcelona must win their final game at home to Eibar and hope Zinedine Zidane’s side lose.
If the teams finish level on points then defending champions Barca will claim a third-straight title because of their superior head-to-head record.
Record-breaking Ronaldo leads Madrid to victory
Ever since Madrid lost 3-2 in a dramatic El Clasico at the Nou Camp in April, this game has been seen as pivotal in the Spanish title race.
Up until Wednesday’s match, Barca had finished every game week top of La Liga following El Clasico, but knew Zinedine Zidane’s side would overhaul them with a positive result at mid-table Celta.
And it was unsurprising that Ronaldo was instrumental. His goals for both Manchester United and Madrid saw him pass ex-Chelsea, Tottenham, AC Milan and West Ham striker Greaves.
Even though the scoreline suggested a comfortable away win, the visitors were pushed by a home side who created chances without taking them.
Celta were punished by Ronaldo’s clinical finishing and when Iago Aspas was sent off for two bookings – the second, rather harshly, for diving – their chances looked over.
Guidetti’s fluky strike looped off Raphael Varane and over keeper Keylor Navas to give them hope, although that was dashed seconds later when Benzema converted Marcelo’s cross.
And, after Ronaldo missed a sitter for his hat-trick, Kroos made sure with a composed low finish.
