Giggs (right) converted an early penalty to give United the upper hand
By Chris Bevan
BBC Sport at Old Trafford
Steven Gerrard was sent off as Ryan Giggs's second-minute penalty proved enough to send Manchester United into the fourth round of the FA Cup, ruining Kenny Dalglish's emotional return as Liverpool manager.
The tie was barely 30 seconds old when Daniel Agger was adjudged to have fouled Dimitar Berbatov in the box and Giggs converted the spot-kick with ease.
Liverpool responded well, but their hopes of a comeback were hit hard when Gerrard was shown the red card for diving in rashly on Michael Carrick just after the half-hour mark.
Despite a spirited effort that offered encouragement to the 9,000 visiting fans, only a succession of fine saves by Pepe Reina kept the game alive until the end.
Roy Hodgson's departure on Saturday had offered Dalglish the opportunity to renew his old rivalry with Sir Alex Ferguson and added extra spice to an already enticing encounter but, 20 years on from his last spell in charge of the Merseysiders, he could not inspire an instant improvement in their fortunes in his first game back in the dug-out.
Dalglish will have easier games in which to make his mark than this one between now and the end of the season.