The La Liga leaders were on top in the all-Spanish tie at Camp Nou before Pau Cubarsi was sent off for bringing down Atletico’s Giuliano Simeone, who was through on goal.
Alvarez whipped home the free-kick and Sorloth doubled their advantage with 20 minutes remaining to give Atletico a strong chance of reaching the semi-finals.
Diego Simeone’s side, who have never won the competition, reached the 2014 and 2016 finals but were beaten by rivals Real Madrid on both occasions.
“We have things to improve and learn from… we’re happy for the win but there’s a long way to go,” Atletico’s Antoine Griezmann told Movistar. “We’re very far from the semis, we’re 90 or more minutes away… we’re confident but keeping our feet on the ground.”
Barca, semi-finalists last season, need to make a huge comeback next Tuesday in Madrid if they are to stand a chance of lifting the trophy they last won in 2015.
“It will be tough there but if anyone can do it, it’s us,” Barca defender Ronald Araujo told Movistar. “We’ve got great players, quality, personality — we will look for the comeback.”
Atletico knocked Barca out of the Copa del Rey in the semi-finals in March and this was the second of three meetings between the sides in a space of a fortnight.
Hansi Flick’s side controlled the game with Atletico talisman Griezmann quiet against his former team, but a moment of clumsiness from Cubarsi dramatically gave the visitors the upper hand before half-time.
The 19-year-old centre-back, chasing Giuliano Simeone as he ran through on goal to reach a ball in behind Barca’s defence from Alvarez, clattered the Atletico coach’s son from behind.
Although referee Istvan Kovacs only produced a yellow card for Cubarsi, he upgraded it to a red after a VAR review.
Worse was to come for Barca, with former Manchester City striker Alvarez whipping the free-kick into the top corner.
Flick tore into the officiating after an incident in the 53rd minute when Barca appealed for a penalty. Goalkeeper Musso appeared to have put the ball in play from a goal kick before defender Marc Pubill handled it inside the six-yard box to retake the goal kick.
Referee Kovacs waved play on and the VAR crew did not call him to the monitor, sparking animated protests from the home bench.
“The VAR was very focused today for Atletico, he’s a German guy, so thanks Germany,” former German national team coach Flick told reporters. “It’s for me a clear red card.”
Flick said the VAR officials should have asked Kovacs to review the incident.
“For my perspective it’s clear, he has to call and say okay come on look at this, the same like before. I don’t understand,” added Flick.
“I haven’t spoken with the referee. I think it was better not to speak with him.
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