Cristiano Ronaldo and Danilo struck within the first 23 minutes for Madrid, who were also grateful to another spectacular goalkeeping display from Keylor Navas to keep Celta at bay yesterday.
Celta were reduced to 10 men just 12 minutes into the second-half when Gustavo Cabral was dismissed for a second bookable offence, but they still pushed Madrid all the way as Nolito set up a grandstand finish five minutes from time when he fired into the top corner.
Victory takes Madrid three points clear of Celta and Barcelona, who entertain Eibar on Sunday.
"We had a lot of chances to finish the game before," said Madrid boss Rafael Benitez.
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"In the end we had to suffer because we needed the third goal, but we have to take the positives which is to come to such a difficult place after playing PSG on Wednesday and get a great result."
Meanwhile, Nolito admitted that Navas had just been too good.
"We have to congratulate him because he stopped three of four clear goals which I don't know how he saved," he told Canal Plus.
That early dominance was rewarded on eight minutes when Lucas Vazquez's cut-back trickled through to Ronaldo who smashed home his 12th goal in as many games this season.
Celta had thrashed Barcelona 4-1 last month and going behind appeared to shock the Galicians back into their early season form as Fabian Orellana forced Navas into his first and arguably best save of the afternoon as he flew to his right to turn the Chilean's volley behind.