Deportivo La Coruna left it late at Camp Nou as they came from two goals down to deny the reigning champions maximum points with a 2-2 draw.
A moment of brilliance from Lionel Messi proved the difference in a tight first half at Camp Nou before Rakitic extended the lead two minutes after the hour mark.
But a late rally from the visitors saw Perez reduce the deficit before setting up Bergantinos for the equalizer four minutes from time.
Only four players survived from Wednesday’s 1-1 draw with Bayer Leverkusen in left-back Jordi Alba, midfielder Ivan Rakitic and forwards Messi and Sandro Ramirez – the latter of whom continued to deputise in the Neymar’s groin-induced absence.
Barcelona enjoyed the lion’s share of possession with their usual flair, but Victor Sanchez’s side coped admirably and went on to create the best chance of the first half as Jonathan Rodriguez was played in behind with a square ball from the right, although Claudio Bravo denied the striker from point-blank range with his leg.
Something out of the extraordinary needed to happen for the deadlock to be broken, and it came from a swish of Messi’s left boot, the Argentine bending a free kick over the wall and into the top-right corner of German Lux’s net.
Similar to the first half, Depor went toe-to-toe with their Catalonian opponents, but Barcelona’s individual quality was the difference, exhibited again in the 62nd minute when Rakitic collected a pass from Messi and lasered in a long-distance shot that went screaming past Lux to make it a 2-0 game.
Deportivo refused to give up though, and nearly halved the deficit in the 75th minute when Miguel Cardoso’s deflected shot bounced off the crossbar. The rebound fell right to Lucas, who headed in, but the linesman flag was raised to annul the goal.
But three minutes later Lucas would get his goal as Cardoso slipped a pass to the La Coruña native who swept a shot in past Bravo to make it 2-1 and a nervy final quarter hour in the Camp Nou.
Finally, in the 86th minute, Barcelona were made to pay for their apathy and carelessness as Deportivo drew level through Álex Bergantiños, who gathered in a pass from Lucas off a counterattack, and rifled past Bravo, much to the despair of the home fans.
A late winner was not to be had by either side as Barcelona now embark for the Club World Cup on the back of three consecutive draws.