It is four games without a goal too for Julen Lopetegui's side, their longest scoring drought since 1985, as Garcia headed home to send the Mendizorrotza Stadium wild.
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Alaves fans ran onto the pitch to celebrate their famous win and the chants continued long after the final whistle blew.
For Madrid this was another body blow and to make matters worse, Gareth Bale, their chief forward threat, had hobbled off injured late on,
The rain came down, the whistles grew louder as Madrid dominated possession but Alaves could have won it sooner when Jony sprinted clear, only to drag his finish wide.
Bale went off and another Alaves chance came in injury time. Courtois came for a cross but failed to gather, allowing Garcia to head in a dramatic winner.