The Dutchman, sent on as a second-half substitute, fired low past David De Gea from Andy Carroll's flick-on to seal Liverpool's berth in the fifth round.
Goals from Daniel Agger and Ji-sung Park had earlier punctuated a pulsating first 45 minutes. The second half, though, yielded little goalmouth action until Kuyt's winner; indeed, both sides appeared to have settled for a draw and an Old Trafford replay. That won't be necessary now.
Anfield is never an easy place to visit and United's task on this clear-but-cold Saturday afternoon was rendered more difficult given the absence of Wayne Rooney, Phil Jones and Nani. The trio all picked up knocks at Arsenal last weekend, while Rio Ferdinand was deemed fit enough only for the bench.
Joining Ferdinand among the substitutes were teenagers Paul Pogba and Michael Keane, while Dimitar Berbatov and Javier Hernandez also had to be content with a place on the bench as Sir Alex turned once again to Danny Welbeck to lead the line.
But all the focus was on Patrice Evra, who, on his last visit to Anfield, was involved in an angry verbal exchange with Luis Suarez, which eventually resulted in the Liverpool forward receiving an eight-game ban for gross misconduct.
Despite the constant booing and abuse from the home fans, Evra carried himself impeccably all day and, in the early stagesat least, he linked well with Ryan Giggs. The latter, facing Liverpool for the 44th time in his career,