But they escaped a worse fate as a late goal for the visitors was ruled out by a VAR review.
The Madrid side went ahead in the 30th minute through a well-worked move finished off by Super Eagles midfielder Oghenekaro Etebo.
But Eibar levelled in the fifth minute of added time at the end of the first half through a header from striker Charles.
Both sides had failed to win either of their first two matches since the season resumed.
But Eibar’s Pedro Bigas thought he had clinched the three points with a glancing header in the 86th minute.
His effort, however, was ruled out for a narrow offside after a VAR review.
The draw keeps Getafe fifth on 48 points, one behind fourth-placed Atletico Madrid who was in action later on Saturday against Real Valladolid.
Eibar is 16th on 29 points, three above Real Mallorca who occupy the final spot in the relegation zone.
“The goal at the end of the first half did us a lot of damage, we had to start again from scratch in the second and we weren’t able to create chances or get the win,” said Getafe striker Jaime Mata.
“We really needed to win this game as we needed a boost after the break-in action. So, we’ll have to keep fighting until we get that first victory.”
Also on Saturday, Espanyol sank back to the bottom of the table after being beaten 3-1 at home by Levante, having climbed above Leganes into 19th in mid-week.
Espanyol has 24 points, three behind 17th-placed Celta Vigo who have a game in hand.
Elsewhere, Athletic Bilbao beat Real Betis 1-0 at home to move into ninth place on 42 points, increasing the pressure on Betis coach Rubi, whose side are 14th on 34 points. (Reuters/NAN)