Despite the bail, Khan, 71, will not be immediately released as he is serving sentences in two other cases
Barcelona, humiliated 2-0 by Hercules in their last league outing, had lost their last two trips to the Calderon but first-half goals from Argentine Lionel Messi and Spain World Cup star Gerard Pique inflicted a first defeat of the season on Atletico.
“We missed several chances and their goalkeeper (David) de Gea had a great game,” said Barcelona striker David Villa.
“In the end the two goals were enough and this is an important win although we have no time to rest as there is another match on Wednesday (against Sporting Gijon).”
It was Barca coach Pep Guardiola’s first win at Atletico, who had a maximum six points before kick-off and his side climbed to fifth a point behind Real Madrid and three points off Valencia.
His joy, however, was tempered by seeing Messi stretchered off in the final minute after having his ankle kicked by Czech defender Tomasz Ujfalusi, who was sent off for the tackle.
Messi is expected to be out for a fortnight after doctors confirmed ligament damage to his right ankle.
Earlier Valencia replaced Real Madrid at the top of La Liga winning 2-1 at promoted Hercules to make it a perfect nine-point start to the season.
Valencia lie two points ahead of Real and Sevilla who came from behind to win 2-1 at Malaga on Sunday thanks to goals from Alejandro Alfaro and Martin Caceres.
It was Atletico’s second defeat in a week following their 1-0 Europa League loss to Aris Salonica, however they stay third in the league above Barcelona on goal difference.
Barcelona were on a high after their 5-1 thrashing of Panathinaikos in the Champions League and had a full strength team with eight Spanish World Cup winners in the starting XI.
Atletico received a boost with forward Sergio “Kun” Aguero shrugging off a knock to start.
Barca took the lead on 13 minutes when Messi flicked the ball into the corner of the net with the outside of his boot after being fed by Pedro Rodriguez.
Atletico responded quickly and were level in the 25th minute when Raul Garcia headed in a Simao corner after goalkeeper Victor Valdes had mis-timed his punch.
Barca took seven minutes to restore their lead with defender Pique finishing like a striker, controlling a Messi corner on his chest and drilling a low shot into the corner for his first goal of the season.
Xavi and Pedro forced Atletico goalkeeper de Gea, only 19 but being tipped for a bright future, to produce two smart saves early in the second half.
Villa could have killed the game off but fired over on 73 minutes and was denied by the terrific de Gea in a one-on-one minutes later.
“Victor Valdes (the Barcelona goalkeeper) came to congratulate me after the game,” said de Gea. “The truth is that Barcelona were superior and we couldn’t do anything.”
Atletico’s Ujfalusi was sent off in the dying seconds for hacking down Messi who clutched his ankle on going down and left the field on a stretcher.
The Atletico defeat means Valencia, league champions in 2002 and 2004, are the only team with a flawless record after a 2-1 win over Hercules on Sunday.
Hercules won 2-0 at Barca last time out but goals from Spanish international Juan Mata and Pablo Hernandez were enough for Valencia, who played most of the second half with ten men following the dismissal of defender David Navarro.
Villarreal climbed up to fifth with a 2-1 win at promoted Levante on Sunday.
Brazilian international striker Nilmar scored a first half brace for Villarreal who sit a point behind third-placed Real.
Despite the bail, Khan, 71, will not be immediately released as he is serving sentences in two other cases
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