Joint-record FA Cup winners Manchester United and Arsenal will meet in the quarter-finals.
United beat League One side Preston North End 3-1 to set up the last-eight clash with holders Arsenal who beat them in the 1979 and 2005 finals. Both clubs have won the famous trophy 11 times.
Giant-killers Bradford City of League One, who caused one of the biggest ever FA Cup upsets by beating Chelsea in the fourth round before seeing off Premier League Sunderland in the fifth, got the home tie their manager Phil Parkinson wished for.
The third-tier side will face Reading, struggling in 16th place in the Championship (second tier) and have a good chance of reaching the last four for the first time since 1911 when they won their only FA Cup. The draw was also kind to Liverpool, who were paired with mid-table Championship side Blackburn Rovers.
England manager Roy Hodgson, who helped make the draw and has managed both clubs, did Liverpool the bigger favour.
Brendan Rodgers’s side are in a rich vein of form after a sluggish start to the season and will be favourites to reach the semi-finals for the first time since they lost the 2012 final to Chelsea.
However, Blackburn have beaten Premier League Swansea City and Stoke City in the last two rounds after coming from behind in both matches. New Aston Villa manager Tim Sherwood will be looking for two victories in four days over local midlands rivals West Bromwich Albion as his side battle against relegation and seek a place in the last four.
Villa and West Brom, who contested three FA Cup finals between 1887 and 1895, will meet at Villa Park on March 3 in the Premier League before the Baggies make the short trip back there for the cup clash. The quarter-finals will be played on the weekend of March 7-8. FA Cup quarter-final draw Liverpool v Blackburn Rovers Bradford City v Reading Manchester United v Arsenal Aston Villa v West Bromwich Albion