Kuyt bundled home from close range in the 37th minute before Davies unwittingly diverted Emiliano Insua's woeful shot into his own net 20 minutes from time.
All this came after Bolton had started positively and almost grabbed the lead in the fourth minute.
Sam Ricketts headed down into the box and Tamir Cohen was left unmarked but, as he was about to fire towards goal, Jose Reina got down to block.
Lone Liverpool striker David N'Gog then tested Jussi Jaaskelainen before Ricketts cleared his header from an Alberto Aquilani corner.
Insua's cross was then inches away from Kuyt's outstretched boot before Bolton came close at the other end on the half-hour.
South Korean winger Chung-Yong Lee embarked on a mazy run from halfway before rounding Reina only for Sotirios Kyrgiakos to get back and clear the danger.
But eight minutes before the break the Reds were in front when Aquilani nodded down Insua's cross and Kuyt scrambled the ball in from four yards.
And the mood of Wanderers boss Owen Coyle got worse just before the break when Lee went down under Insua's challenge but was harshly booked for diving by referee Steve Bennett.
N'Gog blew a golden chance to make it 2-0 eight minutes after the break when he somehow fired a shot against the woodwork after Jaaskelainen had saved Steven Gerrard's shot.
On the hour Jaaskelainen beat out a fierce Gerrard drive but he could nothing about Liverpool's second 20 minutes from time.
Insua's 25-yard shot was heading harmlessly wide until it hit Davies and flew beyond the reach of the Bolton shot-stopper.
Substitute Ryan Babel fired over in the closing stages and Maxi Rodriguez came within inches of sliding in Insua's cross for his first goal for the club but the damage had already been done.