Kuyt punished poor Manchester United defending in the 88th minute, lashing a low shot past David de Gea to send Anfield into raptures after United had failed to deal with a Pepe Reina goal kick.
The Dutch forward’s late winner was the dramatic final act of a largely trouble-free first meeting between the clubs since the acrimony of the Luis Suarez racism affair earlier this season.
The game had seemed set for a replay at Old Trafford after South Korean midfielder Park Ji-Sung had swept in a deserved equaliser for United to cancel out Daniel Agger’s opener for Liverpool.
The build-up to the match had been marked by appeals for calm from United manager Sir Alex Ferguson and his Liverpool counterpart Kenny Dalglish.
United captain Patrice Evra, who Suarez had been found guilty of racially abusing during their league game in October, was booed relentlessly throughout.
But the contest was played out in a good spirit, with referee Mark Halsey brandishing only one yellow card throughout.
Liverpool had taken the lead on 21 minutes when a corner from Steven Gerrard was nodded home by defender Agger.
United’s Spanish goalkeeper de Gea was at fault for the goal, stranded in no-mans-land as Agger headed in.
But United, who dominated possession throughout the opening half, drew level six minutes from half-time.
A deft flick from Antonio Valencia released Rafael down the right who crossed for the byline for Park, the midfielder driving in a low shot first time to beat Reina for 1-1.
With a replay looming, Reina launched a hopeful long goal-kick forward. Andy Carroll got the flick-on and Kuyt pounced to rifle home only his second goal of the season.
In the other early kick-off, Chelsea meanwhile booked their place in Sunday’s fifth round draw after a disputed penalty settled another match which failed to live up to its potentially explosive billing at Loftus Road.
The game was the first meeting of the two sides since the stormy clash in October which led to Chelsea captain John Terry being accused of racially abusing Anton Ferdinand.
Rangers defender Ferdinand was spared the awkward dilemma of whether or not to shake Terry’s hand in the pre-match build-up after the FA ruled there would be no handshake shortly before kick-off.
A disappointing fourth round tie was settled on 62 minutes when Chelsea midfielder Juan Mata sent Paddy Kenny the wrong way from the penalty spot.
However Rangers were seething at referee Mike Dean’s decision to award a penalty, the official ruling that Clint Hill had fouled Daniel Sturridge as the two players came together in the box.
Television replays later suggested Hill had made only the slightest contact with Sturridge, but Dean remained unmoved by QPR protests and Mata stepped up to coolly stroke home the winner. – Sapa-AFP