Diego opened the scoring with a sensational strike from distance only to see his fellow Brazilian level matters off a sublime Andres Iniesta pass.
It appeared as though the visitors would take a slender lead from the quarterfinal encounter at Camp Nou on Wednesday after the Brazilian struck.
Diego had started on the bench, but was called upon in the first half when Diego Costa – who overcame a knee injury to start the match – had to exit. And he duly lit up a match that proved every bit as tight as the teams' respective positions in La Liga suggested with a rasping drive from 25 yards.
However, Brazil international Neymar ensured Gerardo Martino's would not head into the return leg at Vicente Calderon with a deficit when he curled past the otherwise excellent Thibaut Courtois with just under 20 minutes remaining.
Diego Simeone's men will still have the advantage of an away goal in that fixture, but the tie remains nicely poised after the first encounter.
The visitors showed no signs of being fazed by a boisterous home crowd in the opening exchanges, with home goalkeeper Jose Manuel Pinto showing the biggest display of nerves, but former Barca man David Villa failed to punish his weak clearance, inexplicably missing the target from 8 yards after being found by Arda Turan.
Center back Gerard Pique was forced off in the 10th minute after falling heavily in an aerial challenge, with Marc Bartra replacing the Spain international.
Despite the setback, Barcelona started showing glimpses of its free-flowing best and Lionel Messi showed superb footwork to escape Miranda before his through ball was collected by Andres Iniesta, who was denied by a great block from Diego Godin.
Atleti was hit with an injury blow of its own as Costa limped off and a subsequent lack of physical presence in its attack helped Barcelona dictate the tempo, but Messi’s tame 5-yard header was the closest the side came before the break.
Indeed, Martino's men were almost caught on the counter, Villa's curling effort from the edge of the box forcing Pinto into a smart low save on the stroke of halftime. Barcelona was met with a dogged Atleti display in the second half, and its tenacity paid dividends in the 56th minute.
Diego skipped cleverly past Iniesta before drilling an unstoppable drive that swerved past Pinto and into the top right-hand corner.
Barcelona sought a quick response, and Sergio Busquets' well-controlled volley from 20 yards almost provided one shortly after the hour mark, but Courtois was equal to the task.
However, there was nothing the Belgian could to stop Neymar leveling matters in the 71st minute. Iniesta's exquisite outside-of-the-foot through ball found the 22-year-old on the left-hand side of the area and he curled a fine strike past a despairing Courtois.
The equalizer buoyed Barcelona, and the visitors had Courtois to thank for ensuring a fourth draw of the season between the two sides, the Chelsea loanee making impressive saves on Iniesta and Messi, the latter of which was a fine diving stop to keep out the Argentina international's superb free kick.