Kostas Manolas scored the late goal that handed Barcelona just their fourth loss of the season in all competitions and first in the Champions League this campaign, while ending any hopes of a Treble for Ernesto Valverde's team. The towering striker was bundled to the floor by an overmatched Gerard Pique, earning the home side a penalty that skipper Daniele De Rossi dispatched coolly.
The Catalan club had arrived the Italian capital with a three-goal lead after winning the first leg 4-1 but that away goal told.
Barca had an opportunity to hit back less than two minutes later after Juan Jesus tripped the on-rushing Messi 25 yards from goal, but the Argentina forward missed the target with the subsequent free kick.
An out-of-sorts Barca still looked as though they would do enough to scrape through as chances came and went for the hosts, but Manolas - who, like De Rossi, had put through his own net at Camp Nou - headed home eight minutes from time to put Eusebio Di Francesco's side in the driving seat.
But the second half proved to be one of the most iconic 45 minutes in Liverpool's history, with goals from Steven Gerrard, Vladimir Smicer and Xabi Alonso levelling the match up by the hour mark.
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The Italians managed to carve out another chance in the 69th minute but Ter Stegen was on hand to keep out Kevin Strootman's effort from distance.
With their tails up, Roma went in search for the second giving little space to the visitors as Patrick Schick saw his glancing header going narrowly wide minutes later.
Roma took the lead after just six minutes when the prolific Edin Dzeko finished smartly past goalkeeper Marc-Andre ter Stegen. They felt hard done by a few of the referee's decisions, but in the end they're still staring at a three-goal deficit against Barcelona's high-powered attack.
In the other game, Liverpool beat Manchester City 2-1 at The Etihad.