The former Tottenham forward struck a 93rd-minute winner for Joaquin Caparros's men to keep alive their hopes of staving off the threat of relegation from La Liga
Los Bermellones began the evening at the foot of the Liga standings and were seconds away from remaining there until Dos Santos fired home from close range to breathe fresh life into their push for survival.
There were signs early on that the Mexico forward could be the man to unlock the Celta defence, as he fired two free kicks on target.
Despite enjoying most of the ball, Joaquin Caparros's men struggled to convert their possession into chances and it was the visitors who were unfortunate not to go into the interval with a lead.
Midfielder Alex Lopez was sent through one-on-one with Mallorca stopper Dudu Aouate, but the Spaniard fluffed his lines and pulled his shot wide of the target.
Celta emerged from the break the stronger side and had a legitimate case for a penalty denied after striker Mario Barmejo went down under a challenge by Pedro Geromel.
Alejandro thought he had given the home side the lead but Celta goalkeeper Javi Varas produced a stunning save to deny the forward.
With 93 minutes on the clock, it seemed certain that the two sides would share the spoils. Dos Santos, however, had other plans and the former Barcelona starlet was well-placed to tap home from three yards following a goalmouth scramble.
Mallorca leapfrog Celta into 19th position, with the visiting side rock bottom in 20th.