Negredo, who is on loan at the Singapore-owned club from Manchester City, was felled by a wild kick from Juan Antonio Rodriguez in the 70th minute at a sun-drenched Mestalla.
He picked himself up and clipped a confident spot kick high into the middle of the goal to lift Valencia to 47 points from 23 matches, two ahead of fifth-placed Sevilla, who won 3-0 at struggling Cordoba on Saturday.
Real Madrid's 2-0 success at home to Deportivo La Coruna on Saturday put them four points clear of second-placed Barcelona, who host Levante later on Sunday (1600 GMT).
Champions Atletico Madrid are a further three points adrift of Barca in third ahead of Sunday's game at Celta Vigo (2000).
(Writing by Iain Rogers, editing by Michael Hann)
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