The Dutch striker nodded home Jermaine Pennant's hanging cross seven minutes from time to snatch all three points for the Reds, after Reading had looked to be heading for a valuable point.
Liverpool came into the game full of confidence after a week in which they had thumped Arsenal and PSV Eindhoven, but Reading's recent form was poor, with only a point from their previous four Premiership games.
But there was no apparent lack of confidence from the home side.
Jose Reina needed to be alert to beat away a John Oster shot on seven minutes and the Liverpool keeper had a minor scare when Steven Hunt tumbled as the pair raced for the rebound, though any optimistic penalty appeals were quickly waved away by Peter Walton.
But it was Liverpool who made the breakthrough on 15 minutes following an incisive breakaway effort.
Spanish defender Alvaro Arbeloa, making only his second Premiership start, headed clear from a Royals free-kick, then ran the length of the pitch to get on the end of a pin-point pass from Peter Crouch, before curling a neat shot beyond keeper Marcus Hahnemann.
Reading nearly offered an immediate response, Kevin Doyle driving a rising shot over the crossbar after a neat one-two with Steve Sidwell.
And Brynjar Gunnarsson, brought in at right-back in place of the inexperienced Greg Halford, dived headlong at a left-foot cross from Oster but just failed to connect in front of goal.
But, two minutes into the second half, Reading did get themselves back on level terms when Gunnarsson found his goalscoring touch. The full-back, whose previous goal forced an FA Cup replay with Manchester United, got ahead of Arbeloa and chested down a clever chipped pass from Hunt, before smashing a low shot in off the far post beyond the reach of Reina.
Hunt then saw a volley deflect wide and Crouch headed against his own crossbar from an Oster free-kick as Reading went for the win.
But, as Reading tired, Liverpool found chances easier to come by. Kuyt squeezed a low pass across the face of an empty goal, but just beyond the outstretched leg of Steven Gerrard and Hunt headed off the line as Pennant looked to get on the end of a Gerrard free-kick.
But Reading's eagerness to get forward ultimately cost them dear, as left-back Nicky Shorey was caught pushing up, allowing substitute Pennant to run into the space he had left behind him.
Pennant's cross was judged to perfection, hung to the far post, where Kuyt escaped his markers to head beyond Hahnemann.