However, results elsewhere mean they slipped back down to the bottom of the table.
The result means that Gregorio Manzano's side will have to beat Real Valladolid at home, and hope that their three relegation rivals - Deportivo La Coruna, Celta Vigo and Real Zaragoza, all lose their final games if they are to stay up.
Atletico showed off their newly-won Copa del Rey trophy to their fans before the game, which was played out in a party atmosphere at the Vicente Calderon.
However, Diego Simeone's side were not able to toast their celebrations with a victory, and could even have lost the game were it not for two great saves by Thibaut Courtois.
The Belgian made a good save early on to deny Javi Marquez, tipping the midfielder's powerful shot from the edge of the area over the bar.
Marquez took another shot from a similar position just a few minutes later, but this time missed the target.
Diego Costa and Radamel Falcao had Atletico's best chances in the first half, but neither forward could make use of them.
Courtois was again called into action at the start of the second half, this time denying Giovani Dos Santos from close range with an outstretched hand.
Mallorca had one final chance when Alan Hutton sent a low ball across goal but there was no one in the danger zone to meet it.
The Scotland international then unintentionally kneed Felipe Luis in the face while the two contested a high ball, causing the Brazilian to leave the pitch on a stretcher.
Mallorca's players and 400 travelling fans were distraught when the final whistle blew.
Although there is still a slither of hope they might survive the drop, they were aware that they had passed up a fantastic chance to gain ground on their rivals.