The ball found its way to Kuyt at the back post after a brilliant aerial pass from Man of the Match Luis Suarez which found Stewart Downing but his glancing volley was kept out by Jussi Jaaskelainen before Henderson finished the job.
In the 52nd minute, Bolton were staring down the barrel of a tenth-straight loss at Anfield when Martin Skrtel headed home Adamâ€™s corner from the top of the six-yard box before the Scotland international struck with his non-preferred right foot from outside the area across Jaaskelainen a minute later to make it 3-0.
The Reds were in complete control and had other chances to score, highlighted by Suarezâ€™ 23rd minute chip over Jaaskelainen which landed on the roof of the net, before the Uruguayan was unable to cut back a shot from an acute angle after some inter-passing with Kuyt with the shot slamming into the side netting in the second half.
With the score at 3-0 prior to the hour-mark, Liverpool enjoyed the remainder of the match by fizzing the ball around to each other and trying to free their forwards up but they did have a lapse in injury time when Jamie Carragher failed to control a long ball directed at Martin Petrov, who pounced on the error before flicking it back to Ivan Klasnic and he put a consolation goal away for the visiting Trotters who have conceded six in their past two matches following their opening day 4-0 win at QPR.
Yellow cards: LIV - nil
BOL - Gretar Steinsson 44â€™, Ivan Klasnic 49â€™