The Londoners, who lost 5-1 to Liverpool in the Premier League on February 8, won with a 16th-minute goal from Alex Oxlade-Chamberlain and a 47th-minute strike from Lukas Podolski before Steven Gerrard halved the arrears with a penalty on the hour.
Arsenal meet Everton in next month's quarter-finals after they beat Swansea City 3-1 at Goodison Park where Roberto Martinez stayed on course to become the first manager to win the FA Cup in successive seasons with different teams.
He led Wigan Athletic to victory over Manchester City in last season's final and those two sides will face each other again in the last eight after the draw was made on Sunday.
On Saturday, Manchester City beat league leaders Chelsea 2-0 while Wigan won 2-1 at Cardiff City.
Although Arsenal's victory meant there would be no all- Merseyside clash in the quarter-finals, there could be another derby after League One Sheffield United ended the 16-match unbeaten run of Championship side Nottingham Forest with a 3-1 win at Bramall Lane.
United will face Sheffield Wednesday in the competition for the first time since they met in the 1993 semi-finals if the latter eventually beat Charlton Athletic in a tie that was postponed on Saturday because of bad weather.
The other last-eight clash is between Sunderland, who ousted Southampton 1-0 on Saturday, and Brighton and Hove Albion or Hull City who meet on Monday.
The quarter-finals will be played on the weekend of March 8/9.
Image: Lukas Podolski celebrates after scoring
Photograph: Shaun Botterill/Getty Images
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