David Villa had given the hosts the perfect start when he netted against his old side in spectacular fashion after just 12 minutes.
Barca then struggled to find their rhythm against a dogged Atleti side and were dealt a huge blow when Messi failed to reappear for the second-half reportedly due to a muscle injury.
However, in his absence, Neymar was the man to rescue the Spanish champions as he came off the bench to head home Dani Alves' cross 25 minutes from time.
Having thrashed Levante 7-0 in manager Gerardo Martino's first competitive match in charge on Sunday, Barca started confidently and had the first clear opening of the game when Pedro's scuffed effort was palmed away by Thibaut Courtois on 11 minutes.
Within 60 seconds though Atleti were ahead thanks to a fantastic piece of counter-attacking play as Villa fed Arda Turan on the left then burst into the box to meet the Turk's cross flush on the volley to power the ball past Victor Valdes.
Moments later the Spanish international nearly punished his former teammates again as he and Diego Costa combined perfectly but this time Gerard Pique recovered just in time to block Villa's effort.
The game then settled down with Barca patiently probing without ever opening up a well-organised Atleti side before the break.
Worse was to come for the Catalans though as Messi didn't reappear after the interval and was replaced by Cesc Fabregas.
Fabregas nearly had an immediate impact when the ball rebounded to him after Courtois had saved smartly from Alexis Sanchez, but a posse of Atleti defenders descended on the former Arsenal man to block his attempt.
Miranda then came within inches of doubling Atleti's lead as he just failed to make contact with Gabi's free-kick.
Neymar was next to be introduced by Martino and it didn't take the Brazilian long to net his first Barca goal as he charged in at the back post to nod home Dani Alves' hanging cross.
Valdes had to be alert to deny Villa restoring Atleti's lead moments later before Xavi fired a free-kick just over for Barca as the game became increasingly stretched.
Courtois was forced to come to Atleti's rescue once more to deny Sanchez with a brave block from point-blank range 16 minutes from time.
However, there was to be no winner on the night, meaning the tie is still very much alive heading to the Camp Nou for the second leg on Wednesday.