Reds pass Benfica with 6-4 aggregate while Man City eliminate Atletico Madrid with 1-0 aggregate in the quarterfinals.
Atletico advanced 4-2 on aggregate in the round of 16, thanks to two goals by Marcos Llorente in extra time and another by fellow substitute Alvaro Morata.
Liverpool stretched their Premier League lead to 13 points by outclassing second-placed Leicester in a 4-0 win on Boxing Day as Manchester United and Tottenham cut the gap on fourth-placed Chelsea.
It is the first time Liverpool have won the competition, which features each continent's champions, and they became only the second English team to lift the trophy.
Arsenal move into fourth spot as they twice came from a goal down with 10 men to beat Aston Villa 3-2 while Manchester United suffer a dismal 2-0 defeat at high-flying West Ham United who finished the weekend fifth.
Stand-in goalkeeper Adrian was the hero as it was his save from Tammy Abraham allowed Liverpool to beat Chelsea 5-4 on penalties.
Liverpool opened its bid to end a 30-year English title drought by beating Norwich 4-1 on Friday, with four goals in the first half against the Premier League newcomers.
Brazil will face either Venezuela or Argentina, for the tournament's semifinals. Brazil had been eliminated by Paraguay the last two times the teams met in the Copa America quarterfinals, in 2011 and 2015, both times in penalty shootouts.
Barcelona's Coutinho scores from the penalty spot early in the second half and added a close-range header three minutes later. Substitute Everton netted a sensational third five minutes from time to clinch a 3-0 victory against Bolivia.
Liverpool will be seeking its sixth European title when it faces fellow English club Tottenham on Saturday in Madrid.
In other games, Arsenal dented Chelsea’s increasingly fragile title pursuit with a 2-0 derby win while Manchester United continued their stirring revival under Ole Gunnar Solskjaer with a 2-1 victory over Brighton & Hove Albion.
Salah has not scored in his last three Liverpool outings and some observers have suggested he looks short of full fitness and sharpness.
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