Malaga were held 1-1 by battling 10-man Real Sociedad on Sunday, which prevented them from taking advantage of Champions League qualification rivals Valencia's 4-0 thrashing at Espanyol earlier in the day.
It looked to be going Malaga's way when Isco put them ahead after 19 minutes with a fine shot from 25 yards that flew into the top corner and Real Sociedad's Mikel Gonzalez was then dismissed before the break after receiving a second yellow card.
However, Xabi Prieto brought Real Sociedad level after 48 minutes with an excellent volley from the edge of the area and although Malaga pressed forward for the winner, they could not put the ball in the back of the net.
The Andalucian club's Qatari owner, Abdullah Al-Thani, has invested heavily, bringing in players like Santi Cazorla and Martin Demichelis in the search for Champions League football, but they have lacked consistency this season and are now a point behind Valencia in fourth.
"It was a game that I was worried about as we had two days less to prepare for the game than our rivals and now we have the feeling that we have dropped two points as we were leading and had a man extra," said Malaga coach Manuel Pellegrini.
"We were not our usual happy selves at home but I still don't think that this means we have lost a place in the Champions League."
A disappointing Valencia crashed at Espanyol, who kept their own European hopes alive with their first win in almost a month.
Valencia had been in good form recently, having picked up a point at the Bernabeu against Real Madrid and qualified for the semi-finals of the Europa League, but they caused little danger against Espanyol, who took their chances well.
Following a slow start with little danger at either end, Espanyol took the lead after 25 minutes, with Cristian Gomez slotting the ball home inside the area after good work from Sergio Garcia on the right wing.
Valencia had little time to respond as just four minutes later they fell further behind, with Joan Verdu firing a delightful left-foot shot into the top corner from 25 yards.
An error from Valencia goalkeeper Vicente Guaita led to substitute Alvaro Vazquez adding another for Espanyol in the second half and then Kalu Uche finished clinically with 11 minutes left to complete the scoring.
Later, a Fernando Llorente header after 12 minutes gave Athletic Bilbao a 1-0 win over Real Mallorca.
It was only the second victory in eight matches for Marcelo Bielsa's side, whose league form has been affected by their exploits in the Europa League, where they beat Manchester United and Schalke on the way to reaching the semi-finals.
Atletico Madrid are level with Bilbao on 45 points after they responded to their defeat by neighbours Real Madrid with a 1-0 victory in their second derby in succession against Rayo Vallecano.
Top scorer Radamel Falcao claimed the game's only goal in the second half but despite the win, they are still a point off sixth-placed Osasuna, who were beaten 1-0 by Real Betis.
At the bottom of the table, Real Zaragoza beat Granada 1-0 and Villarreal drew 1-1 with Racing Santander.
On Saturday, Cristiano Ronaldo and Lionel Messi both hit their 41st league goals of the season as Real Madrid and Barcelona beat Sporting Gijon and Levante respectively.
It means Real keep their four-point lead at the top of the table ahead of the Clasico showdown next weekend at Camp Nou.