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A Lionel Messi free kick and a bullet strike from Ivan Rakitic put Barca comfortably in control but they eased up in the closing stages and Deportivo took advantage.
Barcelona let a two-goal lead slip with late strikes from Lucas Perez and Alex Bergantinos giving Deportivo La Coruna a 2-2 draw in La Liga on Saturday.
A Lionel Messi free kick and a bullet strike from Ivan Rakitic put Barca comfortably in control but they eased up in the closing stages and Deportivo took advantage.
The Argentine curled the ball into the top corner of the goal from 25 metres to break the resistance of a well organised Deportivo after 38 minutes.
Rakitic fired home from similar distance in the 62nd before in-form Lucas pulled a goal back for the visitors after 77 and Bergantinos equalised four minutes from the end.
It is the second successive draw in the league for Barca who lead the table with 35 points from 15 games while Deportivo, who have been a surprise this season, are in sixth on 23.
Second-place Atletico Madrid, on 32 points, face Athletic Bilbao on Sunday when Real Madrid, in third with 30, have a tough match away to Villarreal.
"It is difficult to explain it," midfielder Andres Iniesta told reporters.
"We lost control when we needed to keep it and made it easy for the opposition at 2-0.
"These things happen and we will analyse it and try and make sure it doesn't happen again."
Injured Neymar was missing from Barca’s ruthless attacking trident and so the door was opened for youngster Sandro Ramirez.
Barca were up against a tactically strong Deportivo, who have one defeat in 12 matches, and their game plan was not to sit too deep but have players forward to take advantage of counter-attacks.
Luis Suarez missed a golden chance early on, firing just wide after being set up by a Sandro header and generally Barca had plenty of the ball but found little space.
Lucas had a shot blocked from close range at the other end before a piece of Messi brilliance gave Barca the lead.
Barca continued to probe but it took another special effort from Rakitic to breach the Depor defence again.
The Catalan side appeared on course for victory but they lost composure at the back allowing in Lucas for his 11th league goal, and then Bergantinos was given space to strike the ball home past keeper Claudio Bravo.
