Madrid-based Rayo took a seventh-minute lead thanks to a brilliant volley from captain Piti before Alejandro Alfaro levelled for the Balearic Islanders five minutes later at the Iberostar Estadi.
Led by Mexico's former Barcelona and Tottenham Hotspur forward Giovani Dos Santos, Mallorca threatened Rayo's goal on several occasions but were ultimately fortunate to avoid defeat.
Rayo's Guinean forward Alhassane Bangoura, known as "Lass", twice hit the post in the second half after Montenegrin team mate Andrija Delibasic struck a shot against the frame of the goal before the break.
The result leaves Mallorca in 18th place on 28 points from 32 matches and they have six games in which to lift themselves out of the relegation places.
Rayo are eighth on 45 points and still have an outside chance of qualifying for Europe.
Leaders Barcelona, 13 points clear of champions and arch rivals Real Madrid, can take a step closer to a fourth title in five years with a win at home to Levante on Saturday.
Real host seventh-placed European qualifying hopefuls Real Betis in an earlier kick-off.