Dean Holdsworth's Shots, currently 11th in League Two, edged League One Rochdale 2-1 in midweek to secure their place in the last 16.
And they have been rewarded with a dream tie at home to the reigning Premier League champions after Sir Alex Ferguson's side comfortably beat Leeds 3-0 at Elland Road.
The draw produced five all-Premier League games, with Wolves hosting Manchester City, Blackburn at home to Newcastle, Arsenal playing Bolton, Stoke entertaining Liverpool and Everton welcoming Chelsea to Goodison Park.
Cardiff will be at home to fellow Championship outfit Burnley while Crystal Palace host Southampton.
All fourth-round ties will be held in the week commencing October 24.
Carling Cup fourth-round draw:
Wolves v Manchester City
Cardiff City v Burnley
Blackburn Rovers v Newcastle United
Arsenal v Bolton
Stoke City v Liverpool
Aldershot v Manchester United
Crystal Palace v Southampton
Everton v Chelsea