All four goals arrived in a 25 minute period in the first-half as Paco Alcacer cancelled out Pablo Sarabia's opener.
Angel Lafita then put Getafe back in front only for substitute Santi Mina to level once more.
A point leaves Valencia still six points off the top four, but does at least preserve their unbeaten home record in the league stretching back to November last year.
Gary Neville appointed Valencia coach: La Liga club
Neville had manged to get his first win in three attempts against third-tier Barakaldo in the Copa del Rey in midweek.
But, just as against Eibar in his first taste of La Liga action last weekend, Valencia make a poor start and were behind after just 10 minutes.
Goalkeeper Jaume Domenech has been Valencia's player of the year so far this season, but he reacted late to Sarabia's free-kick and couldn't prevent the ball finding the top corner despite getting a hand to it.
However, the hosts reacted quickly to going behind as Alcacer caught Joao Cancelo's cross from the right sweetly to register his seventh goal of the season.
Copa del Rey: Mina, Negredo gift Neville first Valencia win
Yet, Valencia were still incredibly open at the back and were behind again midway through the half when Lafita smashed home a loose ball after Shkodran Mustafi had appeared to upend Victor Rodriguez inside the box.
Getafe centre-back Cala had another goal marginally ruled out for offside moments later as the home fans began to turn on their side.
And it seemed Neville had suffered another setback when Jose Luis Gaya had to be replaced through injury.
Yet, that proved to be a blessing in disguise as Mina replaced the full-back and equalised with his first touch as he swept home Alcacer's cross at the back post.
The hosts then looked the more threatening side for large spells, but were denied by former Valencia 'keeper Vicente Guaita as he produced great saves to deny Danilo and Dani Parejo either side of the break.
Neville through on former Manchester City striker Alvaro Negredo in the search for a winner and he had a golden chance when he headed straight at Guaita three minutes from time.
Yet, in the end, Valencia were lucky to even get a point as Getafe passed up a series of chances on the break in the final few minutes with Lafita hitting the bar two minutes into stoppage time.
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