Granada, who sit second-bottom in the Spanish top flight, missed a chance to move within one point of safety on Wednesday after Theo Bongonda's 93rd-minute leveller for the visitors.
A draw will still be seen as a decent result against 11th-placed Celta, but to come so close to winning and fail will rankle with Granada coach Abel Resino.
Looking to bounce back from Sunday's 9-1 humiliation at Real Madrid, Granada made an excellent start.
Robert Ibanez gave them the lead in the third minute but in a fiery match, that saw 12 cards dished out, they saw their hopes slashed just before the half-time break.
Granada defender Jeison Murillo - who was initially booked in the 39th minute - was given a second yellow card just three minutes later.
Celta looked like heading home with nothing though, until substitute Bongonda struck at the death to frustrate the hapless hosts.
