After fourth-placed Valencia drew 2-2 at Real Madrid on Saturday, a win for the champions would have propelled them six points clear in third with two games left but they slipped up against a team fighting for their top-flight status.
David Barral tapped in at the far post in the 32nd minute to put 14th-placed Levante ahead at their Ciutat de Valencia stadium before Guilherme Siqueira levelled with a smart volley three minutes later.
Atletico fell behind again in the 63rd minute when Kalu Uche bundled the ball over the line and Torres secured a point when he nodded powerfully home following a corner 10 minutes from time.
"We knew what it means to play here, where Levante are very strong," Siqueira told Spanish television.
"In this final part of the season every point is crucial," added the Brazilian. "We have two games left to make sure of the third spot that we want."
Atletico have 77 points from 36 matches, with Valencia on 73 in fourth, which carries a berth in qualifying for Europe's elite club competition.
Leaders Barcelona (90 points) are on the brink of a fifth title in seven years after they won 2-0 at home to Real Sociedad on Saturday to stretch their advantage over Real Madrid (86) to four points.
This weekend's matches are being played under the cloud of a possible strike orchestrated by the Spanish football federation (RFEF) and the players’ union (AFE) due to a dispute over a new law on collective bargaining for the sale of television rights.
The two organisations, who complain the law does not take their interests sufficiently into account, have threatened to halt games from May 16, meaning the last two La Liga match days and the King's Cup final between Barca and Athletic Bilbao are under threat.
(Editing by Ed Osmond)
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