The other semi-final sees Aston Villa take on the winner of Blackburn and Liverpool’s replay after the pair drew 0-0 at Anfield on Sunday.
Arsenal’s Danny Welbeck scored on his return to Old Trafford to seal a 2-1 victory for the 2014 FA Cup winners after Wayne Rooney had cancelled out Nacho Monreal’s opener.
That has set up a clash with Sky Bet League One Bradford, who knocked the Gunners out of the Capital One Cup in 2012, or Steve Clarke’s Reading.
Villa secured their place in the semi-finals for the first time since 2010 by seeing off local rivals West Brom 2-0 in a fiery affair on Saturday and Tim Sherwood’s side will now be waiting to see whether Liverpool or Blackburn are their Wembley opponents for a place in this season’s final.
FA CUP SEMI-FINAL DRAW
Bradford/Reading v Arsenal
Aston Villa v Liverpool/Blackburn
Ties to be played at Wembley on April 18/19.