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.
Cristiano Ronaldo breaks another record as Real Madrid thrashed Celta Vigo
Reviewed by Debo Olowu
on
May 17, 2017
Rating:
Reviewed by Debo Olowu
on
May 17, 2017
Rating:
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