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With Roma and Ajax only separated by away goals with 20 minutes remaining, Dzeko steered home after great work from Riccardo Calafiori to give the Giallorossi a sliver of breathing space in the tie.
And that proved crucial, as the game at the Stadio Olimpico eventually finished 1-1 - ensuring a 3-2 aggregate win for Paulo Fonseca's side after last week's 2-1 win in Amsterdam.
Substitute Brian Brobbey scored moments after half-time for the visitors, but the second goal they needed to have any hope of progressing would not prove forthcoming.
In truth it was Ajax who controlled large parts of the contest, dominating possession - especially in the first half - and probing for opportunities.
It was not until Brobbey came on, however, that they found a way to break the deadlock. The young striker latched onto a deep ball into space to flick home, setting up a dramatic final 40 minutes.
Soon after Dusan Tadic thought he had put his side ahead in the tie, only for the goal to be ruled out for a foul in the build-up. It was a let-off for the Giallorossi, who certainly made the most of it.
Dzeko's goal - after a great run and cross from Calafiori - did not change the task for Ajax manifestly, but now another goal for them would only be enough to force extra-time, not win the tie outright. And that added security seemed to calm Roma - who did not have too many real scares as they saw out the contest.
The Giallorossi will now face Manchester United for a place in the final of this season's competition.
First up, however, they are back in Serie A action - as they travel to face Torino on Sunday.
ROMA 1-1 AJAX (3-2 agg.)
GOALSCORERS: Dzeko (72'); Brobbey (49')
ROMA (3-4-2-1): Pau Lopez; Mancini, Cristante, Ibanez; Karsdorp, Diawara, Veretout, Calafiori (Villar); Mkhitaryan (Pedro), Pellegrini; Dzeko (Mayoral)
Unused subs: Mirante, Fuzato, Santon, Perez, Ciervo, Darboe, Morichelli
AJAX (4-3-3): Stekelenburg; Klaiber (Schuurs (Idrissi)), Timber, Martinez, Tagliafico; Alvarez (Kudus), Klaassen, Gravenberch; Antony (Brobbey), Tadic, Neres (Traorè)
Unused subs: Scherpen, Kotarski, Ekkelenkamp, Kasanwirjo, Timber
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