Last season's Segunda Division winners were on course for a first victory since January after Mikel Arruabarrena's 35th-minute penalty, but trailed by the break as they failed to put distance between themselves and their relegation rivals.
Arruabarrena opened the scoring from the spot 10 minutes before the interval to register his side's first goal in almost a month after Federico Piovaccari was felled by Cristian Alvarez.
However, the opener was followed by a swift collapse as Alberto Bueno registered his eight goal in five games to level soon after.
The turnaround was complete when Manucho glanced home a corner three minutes prior to the interval.
A goalless second half ensured Rayo move into the top half with a third straight league win, while Eibar look nervously over their shoulder at the drop zone just three points beneath them.
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'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
