It appeared as though the visitors would take a slender lead from the quarter-final encounter at Camp Nou on Wednesday after Atletico's Brazilian midfielder 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 play.
And he duly lit up a match that proved every bit as tight as their respective positions in La Liga suggested with a rasping drive from 25 yards.
However, Brazil international Neymar ensured Gerardo Martino's side 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, 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 eight yards after being found by Arda Turan.
Centre-back Gerard Pique was forced off in the 10th minute after falling heavily in an aerial challenge, Marc Bartra replacing him.
Despite the setback, Barcelona started showing glimpses of their free-flowing best and Lionel Messi showed superb footwork to escape Miranda before his throughball was collected by Andres Iniesta who was denied by a great block from Diego Godin.
Atleti were hit with an injury blow of their own as Costa limped off and a subsequent lack of physical presence in their attack helped Barcelona dictate the tempo, but Messi’s tame five-yard header was the closest they went 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 half-time.
Barcelona were met with a dogged Atleti display in the second half, and their tenacity paid dividends in the 56th minute.
Diego skipped cleverly past Iniesta before drilling an unstoppable drive which 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 levelling matters in the 71st minute.
Iniesta's exquisite outside-foot throughball found the 22-year-old on the left-hand side of the area and he curled a fine strike past a despairing Courtois.
The equaliser 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 from Iniesta and Messi, the latter of which was a fine diving stop to prevent the Argentina international's superb free-kick finding the net.
