Ramires and Victor Moses scored in the second half as Rafa Benitez's team triumphed 2-0, to line up Sir Alex Ferguson's sixth FA Cup tie against the West London side.
The quarter-final at Old Trafford on Sunday 10 March (kick-off 16:30 GMT) will be the clubs' first meeting in the competition since the 2007 final, when an extra-time goal by Didier Drogba snatched glory for Chelsea, then managed by current Real Madrid boss Jose Mourinho. However, the Reds have much the better record in FA Cup contests, having beaten the Blues emphatically, 4-0, in the 1994 final and knocked them out in 1996 (semi-final), 1998 (third round) and 1999 (quarter-final replay).
United will hope for better fortune against Chelsea in the FA Cup after losing a nine-goal thriller to the same opponents in the Capital One Cup earlier this season at Stamford Bridge. A fourth clash for 2012/13 is due in early May, when the Blues will return to Old Trafford for the Reds' penultimate home match in the Barclays Premier League.