Liverpool deserved the win, although Bolton did give them the odd scare in the second half when they upped the ante.
Dutchman Kuyt opened the scoring on 28 minutes, with his head, after he had connected to Fabio Aurelio's pin-point left-wing delivery.
That could have been the striker's second because he had hit the bar from 14 yards out just seven minutes earlier.
But one man who should definitely have made it two was Robbie Keane, who failed to connect with the ball from just one yard out soon after the goal.
Despite winning their last two games against Manchester City and Hull City, Wanderers have been struggling to score goals this season.
They had only scored 11 goals in 12 matches before this one, and six of those came in two wins over Stoke and West Ham.
Defender Gary Cahill then had a header ruled out on the stroke of half-time because captain Kevin Nolan was impeding Jose Reina.
Wanderers came out for the second half with much more purpose, as substitute Ricardo Gardner, Nolan and Kevin Davies all went close.
Davies actually played Gardner, on for Fabrice Muamba, through, but the Jamaican winger slipped after pushing the ball slightly too wide in his attempts to round Reina.
Reds defender Daniel Agger then collided with the post, and appeared to lose a tooth.
Gerrard then should have doubled the visitors lead when he made a bad contact with sub Fernando Torres' cross after sliding in at the far post.
But with 17 minutes left on the clock the skipper, and England midfielder, did make the game safe when he glanced home, with his head, the Spaniard's exquisite ball with the outside of his right boot.