A deep cross was headed goalwards by striker Tomer Hemed in the 93rd minute and when keeper Javi Varas could only parry the effort, Mexico forward Dos Santos volleyed in the rebound to set off ecstatic celebrations on the pitch.
The victory moved Mallorca up to second from bottom with 27 points and seven games left, behind Real Zaragoza on goal difference.
Promoted Celta, who now prop up the table on 24 points, have taken one point from their last six games.
Mallorca dominated the early exchanges and Dos Santos was the most dangerous player, going close with two free kicks and delivering a corner that was headed just over the bar.
However, it was Celta who had the clearest chance before the break when Alex Lopez fired wide with only the keeper to beat.
Celta grew in confidence in the second half as Borja Oubina volleyed over and home keeper Dudu Aouate saved a point-blank header from Andres Tunez.
The home side showed more desire to seek a winner in the closing stages and were rewarded when former Tottenham Hotspur forward Dos Santos scored.
- Sports & Recreation