The Brazilian struck in the second half to ensure both sides took home a share of the spoils in a tight affair
The Brazilian's 66th-minute header cancelled out David Villa's opener at the Estadio Vicente Calderon to set up a tantalizing second leg.
Villa's goal was also his first for his new club and came against his former side but Barcelona will go into the return tie on August 28 with the upper hand.
Whether Barca superstar Lionel Messi is available for that clash, however, remains to be seen after he came off at halftime with a suspected hamstring injury.
It was Villa who struck with the first real chance of the game as his brilliant finish put Atleti ahead on 12 minutes.
A sweeping counterattack led to Villa playing a clever pass out wide to Arda Turan and the Turkey international returned the ball to his 31-year-old team-mate.
Just inside the area, Villa's volley was exquisitely controlled and found the bottom corner for his first goal for los Rojiblancos.
Barcelona characteristically controlled possession but struggled to create much against a well-drilled Atletico defense.
Making matters worse for Barca, Messi made way at halftime and was replaced by Cesc Fabregas.
The former Arsenal captain went close to an equalizer four minutes into the second half, moments after Alexis Sanchez was denied by Thibaut Courtois in a one-on-one.
After the Chilean's effort was kept out, he set up Fabregas, who was unable to get a shot away under a last-ditch tackle from Turan.
Clear-cut chances were few and far between for Barca and Andres Iniesta tried his luck from range but his effort was comfortably saved by Courtois.
Diego Costa forced Victor Valdes into a save on the hour-mark before Barcelona equalized through Neymar six minutes later.
The Brazil star had been introduced just seven minutes before he headed in a Dani Alves cross at the back post, after the right back exchanged passes with Xavi.
Alves' cross was perfectly weighted and Courtois was unable to get across quick enough to keep the header out at his near post.
Barcelona looked the more likely to find a winner and saw Xavi curl a free kick just over on 72 minutes.
Courtois came out quickly to block a Sanchez shot at the back post minutes later as the visitors took control of the contest.
A tired-looking home side was pinned back into its defensive half but it remained compact enough to keep Barcelona at bay and set up an intriguing second leg at Camp Nou.