Karim Benzema opened the scoring yesterday before a late double from Cristiano Ronaldo sealed the win as Celta were made to pay for passing up a host of clear-cut chances.
With the scoreline still deadlocked with an hour played, Real boss Carlo Ancelotti introduced the fit-again Gareth Bale and Jese Rodriguez from the bench in the search of a goal.
The Italian was rewarded when Jese squared for Benzema to break the deadlock 23 minutes from time.
And Ancelotti accepted that his side had been far from their best on their return to competitive action after a two-week lay-off.
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"We didn't play well, especially in the first-half. Our play was slow, but that is quite normal that after a break the team doesn't have the same rhythm.
"In the second-half our intensity was better and we came through the game well in the end."