Iran Press/Europe: Without the suspended Jude Bellingham, Madrid led when Vinicius Jr stabbed in from close range after his first effort was blocked by Celta keeper Vicente Guaita.
It was the least Carlo Ancelotti's side deserved after a dominant first half.
The hosts were sloppier after the break - to the frustration of the Bernabeu fans - but Celta were unable to take advantage.
Madrid missed chances through Rodrygo and Brahim Diaz before they wrapped the game up with three goals in the final 11 minutes.
They got the first of those late goals from another set-piece when an unmarked Antonio Rudiger headed against the bar and the ball rebounded in off former Crystal Palace keeper Guaita.
That ended Celta's resistance and moments later another defensive mess led to the third goal.
Vinicius' cross from the left caused havoc between Guaita and Carlos Dominguez, with the defender haplessly diverting an attempted clearance into his own goal.
Turkish teenager Arda Guler then netted his first Madrid goal by slotting in from a tight angle moments after coming on the pitch as a substitute.
With nearest challengers Girona and Barcelona winning earlier this weekend, Madrid could not afford to offer hope to their rivals with a slip against relegation-threatened Celta.
Dropping points rarely looked likely but the tension which had lingered into the final half-hour disappeared with the three late goals.
The demanding Bernabeu crowd's exasperation seemed to result from a second home game in five days where their team did not put away the visiting team as they would have hoped.
Los Blancos were far from their best when they scraped past RB Leipzig on Wednesday to reach the Champions League quarter-finals.
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