Roma went on to dominate for the balance of the first half and would have increased their advantage if Czech international Patrik Schik hadn't squandered a pair of good chances before Barcelona keeper Marc-Andre ter Stegen stopped Dzeko's header in the 37th minute.
Despite conceding the goal, Barcelona went to the dressing room leading 4-2 on aggregate and betrayed no sign of panic.
The hosts began the second half where they left off, remaining firmly on the front foot against a strangely passive Barça side.
In the 58th minute, Gerard Pique fouled Dzeko in the box and the referee awarded a penalty, converted by captain De Rossi to bring Roma within one goal on aggregate.
Ter Stegen came up with a great stop in the 79th minute on a strike by late substitute Stephan El Shaarawy, but Greek defender Manolas scored on a header three minutes later to leave the teams knotted 4-4 and Roma saw out the match.
"I'm happy for the lads but it wasn't the formation: the difference was in our mindset and aggressive approach. We decided to go with three forwards close together because it meant they had less width and we could get at them more," Roma chief coach Eusebio Di Francesco was quoted as saying by the club's website.
"I'm very happy with the new formation but I'm more interested in the way the team plays. We must take strength from this."
FC Barcelona chief coach Ernesto Valverde said in a statement: "They took risks and we couldn't cope with all that deep pressing. The first goal gave them strength and then they got a second and third in the second half."
"I feel sorry for the fans. It's been a huge disappointment for them. But now we just have to focus on the competitions that we have left. We have to keep looking ahead."
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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