But Valencia made it 1-1 seven minutes into the second half through Antonio Barragan's deflected shot.
And Otamendi then powered the ball in from a corner to leave Madrid's place at the top of La Liga under threat with Barcelona playing Real Sociedad later.
It was Real's first defeat since they lost to city rivals and La Liga champions Atletico Madrid on 13 September.
They will concede top spot to Barcelona if the Catalans beat David Moyes's Sociedad on Sunday night.
The result lifted Valencia, beaten just once at home all season, into the Champions League place
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