Liverpool will play Real Madrid in the Champions League final later this month after beating Roma 7-6 on aggregate.
The Reds, 10/1 with Sky Bet at the start of the season to reach the Kiev showpiece, lost 4-2 to the Serie A side on the night.
That was despite taking the lead on two occasions, and they were fairly comfortable before conceding a late Radja Nainggolan double.
Jurgen Klopp's side laid the foundations in the first leg last week with a 5-2 victory and they will now face European giants Real Madrid on May 26.
The Merseysiders will be hoping to stop Zinedine Zidane's side, who sealed their place in the final after beating Bayern Munich, from winning the competition for a third successive year.
Sadio Mane opened the scoring inside ten minutes before Roma were level after a fortuitous deflection saw James Milner put the ball into the back of his own net.
Georginio Wijnaldum headed the visitors back into the lead on 25 minutes and Dzeko continued his good record against the Reds by drawing the Italians level early in the second half.
Liverpool did not maintain the intensity of the opening half hour, but they managed the game well and were not fazed after conceding Nainggolan's two goals, which proved to be too little too late.
The first was a low strike from the edge of the box which beat Loris Karius, then in stoppage time the hosts were awarded a penalty after Ragnar Klavan handled in the box, with the Belgium midfielder duly converting the resulting spot-kick.
Champions League final odds - to win outright (via Sky Bet)
Real Madrid - 8/11
Liverpool - 11/10
Post-match reaction (via BT Sport)
Liverpool boss Jurgen Klopp: "The boys deserve it. The campaign, the character they showed, the mentality they showed, the football they showed - that's just crazy.
"And then it suits our situation, what was it? On aggregate it's - I forgot it - 7-6, it was unbelievable.
"To be honest, there's a lot of room for improvement in our general defending.
"We were constantly under pressure. Each counter attack was really dangerous but we didn't use them, we are usually much better. We wanted to do it, without doing the right thing.
"It was the first semi-final for most of the boys and it's completely normal that you have to keep your nerves and all of that stuff.
"It was a little bit exciting, more exciting than what I actually want but now it's over and I'm fine."
Liverpool skipper Jordan Henderson: "We never do it the easy way, unfortunately. Amazing effort. We knew it'd be tough coming here.
"I thought in the first half, we did well and scored some good goals. We could have been a bit more clinical on the counter attack but overall I thought we handled the situation well, apart from the last 10 minutes of the second half - and concede the late goals like we did - so we need to stop that but overall we're delighted to be in the final.
"We knew it was important to get that first goal and to get one early on was brilliant.
"A little bit unlucky with their first goal. But overall, first leg, second leg, I think we're going to be happy with what we've done.
"Of course, we could have been a lot better here in this leg, but overall we're just pleased to get through to the final. We've been entertaining I think."
Georginio Wijnaldum added: "It's going to be a nice game. If you want to win the Champions League you have to beat anyone and everyone.
"Real Madrid are a tough opponent with a lot of important players but we have them also - so it's going to be a good match."
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Page last updated at 2305 BST 02/05/2018.
