Liverpool had trounced Arsenal 5-1 at Anfield in the Premier League last weekend, but the London club took revenge through goals in each half by Alex Oxlade-Chamberlain and Lukas Podolski.
Steven Gerrard cut Arsenal’s lead in half with a 59th-minute penalty after Podolski tripped Luis Suarez.
But Liuverpool should have have a second penalty moments later when Oxlade-Chamberlain brought down Suarez, but somehow referee Howard Webb missed the call.
Everton’s reward for a fifth round FA Cup win over Swansea was a tough quarter-final draw away to Arsenal, but manager Roberto Martinez will be pleased with the showing of recent signing Lacina Traore.
The Toffees advanced into the last eight with a 3-1 win over another Premier League side in the Swans at Goodison Park.
Martinez, who won the Cup with Wigan last season, saw Lacina Traore, his loan transfer signing from Monaco in January, take just four minutes of his debut to give the Merseysiders the lead.
Jonathan de Guzman drew Swansea level in the 15th before second half substitute Steven Naismith put Everton in front again — with his fourth goal in six games — and then won the penalty from which Leighton Baines scored to put the result beyond doubt.
Sunday’s other Cup tie saw third tier Sheffield United beat second-tier Nottingham Forest 3-1.
United, managed by former Forest favourite Nigel Clough, could be involved in a derby quarter-final against Sheffield Wednesday if their city rivals beat Charlton Athletic in a re-arranged match.
Jamie Paterson headed Forest into an early lead before the on-loan Conor Coady drew the Blades level in the 66th minute.
And Chris Porter then sparked scenes of near delirium amongst the Bramall Lane faithful with two goals right at the end of the match.
He put them in front with a 90th minute penalty following Greg Halford’s handball and then sealed victory in stoppage-time with a finish from close range.
The last eight line-up also saw FA Cup holders Wigan paired against Manchester City in a repeat of last season’s final.