The result leaves Barca eight points clear at the top, with a chance for the rampant leaders to stretch their lead to 11 points with eight games left when they play at Villarreal on Sunday.
Atletico, who have been drawn to meet Barcelona in the quarter-finals of the Champions League, will be kicking themselves for offering such a gift to their title rivals after Antoine Griezmann had given them a 29th-minute lead with a superb free kick.
With a fifth consecutive league win seemingly in their grasp, Antonio Sanabria shocked them with a 79th-minute equaliser, also from a free kick, before Castro put the finishing touch to Jony's low cross with one minute left on the clock.
The defeat came after an exhausting week for Diego Simeone's men, who had secured their last-eight spot in the Champions League only after two hours of football and a mentally-draining penalty shootout against PSV Eindhoven on Tuesday.
Simeone was evidently not happy that the league schedule meant his side had to play on Saturday afternoon while their title rivals Real Madrid, who were not in European action this week, and Barcelona were given the chance to play 24 hours later.
"But I do not like to look for excuses," Simeone told reporters. "We have always been aware of our goal. The aim of the club is to be third and we work in order to reach the club's goal. We know this defeat make things much tougher for us to have any chance to be champions."
The win briefly hauled Gijon out of the bottom three on goal difference but Rayo Vallecano and Granada later fought out a 2-2 draw and both moved a point clear of the 19th-placed club.
Ze Castro scored an equaliser three minutes from time to earn Rayo Vallecano the crucial point against a Granada side who had been forced to protect a 2-1 lead for the last 20 minutes with 10 men after a second yellow card shown to their Nigerian striker, Isaac Success.
A goal from Brazilian Willian Jose six minutes before the interval earned Las Palmas a 1-0 win at Real Sociedad to move them closer to guaranteed safety, five points above the relegation zone.
(Reporting by Ian Chadband, editing by Alan Baldwin and Clare Fallon)
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