Sergio Ramos's towering first-half header put the visitors in front, but Las Palmas looked to have salvaged the point their performance deserved through Willian Jose three minutes from time yesterday.
However, Casemiro punished some atrocious marking to head home the winner before Ramos was sent-off for the 20th time in his Madrid career late on.
Elsewhere, Valencia boss Gary Neville's troubles continued as he branded his side's performance 'unacceptable' in losing their local derby 1-0 to Levante.
And Sevilla maintained their hopes of Champions League football next season with a thrilling 4-2 win over Villarreal.
Madrid goalkeeper Keylor Navas had been on top form as Real saw off Roma to reach the Champions League quarterfinals in midweek and was consistently called upon to save his side in the Canary Islands.
"I go away happy with the result, but a little worried with what I saw in the second-half," said Madrid boss Zinedine Zidane.

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