Getafe's 37-year-old striker Jorge Molina broke the deadlock by netting on the rebound in the 58th minute and then doubled their advantage in the 67th, waltzing his way past three Valencia defenders before firing home.
Molina's strike partner Jaime Mata added a third goal in the 88th minute after Valencia's new signing Alessandro Florenzi had been sent off with a straight red card.
They visit champions Barcelona next Saturday.
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Valencia are five points behind the Madrid side in fifth.
The rivalry between the two clubs has been cranked up in the last year after Valencia won a bitter Copa del Rey quarter-final tie in stoppage time last season and pipped the Madrid minnows to fourth place in the standings to snatch a Champions League spot.
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"We played a fantastic game, I'm so happy with the players because we have overcome an all-powerful Valencia side," Getafe coach Jose Bordalas told reporters.
"We were up against a team with a budget far bigger than ours and we beat them comfortably."
Valencia defender Gabriel Paulista was fiercely critical of his side, who beat Barca two weeks ago but were knocked out of the Copa del Rey by Granada on Tuesday before being outclassed by Getafe.
"The elimination to Granada was hard to take and today was a chance to start winning again but everything went wrong for us," he said.
"We have to change our attitude, we have to be tougher on the pitch and fight more, we also need to be more convincing in every aspect."
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