Ronaldo, 32, 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.
“The most difficult part is still to come even though we’re getting closer to the title every day,” Madrid manager Zinedine Zidane said.
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.
| Selected leading European goalscorers (league goals) | |
|---|---|
| 366 | Jimmy Greaves (Chelsea, AC Milan, Tottenham, West Ham) |
| 365 | Gerd Muller (Bayern Munich) |
| 346 | Lionel Messi (Barcelona) |
| 317 | Steve Bloomer (Derby, Middlesbrough) |
| 310 | Dixie Dean (Tranmere, Everton, Notts County) |
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.
Any hope for Barca?
Madrid have won six-straight games since their Nou Camp defeat, therefore keeping the title race in their own hands.
Barcelona have matched them every week with victories of their own, but Real’s relentless form means the Catalan club are now relying on Malaga to do them a favour on Sunday.
However, there is one result that gives Barca hope of their title rivals slipping up… their own defeat at Malaga on 8 April.
Neymar was sent off as a 2-0 defeat hampered Luis Enrique’s hopes of leaving the Nou Camp with another league title on his CV.
‘I don’t feel like we’re champions yet’ – reaction
Real Madrid manager Zinedine Zidane
We have one game left but today was very important. We know what we need to do. We need to prepare well and recover from today as we gave so much.
The first half was end to end and that doesn’t suit us, we were much better with the ball in the second and we played a little better.
I don’t feel like we’re the champions yet, we still need to pick up more points and keep on with what we’re doing.
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