Wanderers slipped to a 2-0 defeat at Anfield after conceding goals in each half.
Dirk Kuyt's close-range tap-in set Rafa Benitez's side on their way on 37 minutes after Sotirios Kyrgiakos had earlier denied Chung-Yong Lee with a superb goal-line clearance.
And in the second-half, Insua's deflected shot from 25-yards sealed the victory for the Reds.
Anfield was never going to be an easy place to come for Owen Coyle's side and although they worked tirelessly, they caught Liverpool on a good day.
Manager Owen Coyle made one change to his starting line-up with Mark Davies returning from injury to take the place of Ivan Klasnic in a 4-5-1 formation.
New signing Jack Wilshere took a place on the substitutes' bench alongside Vladimir Weiss who impressed in the final few minutes of his debut against Burnley.
Again it was another bright start from Wanderers, who perhaps with a bit more fortune inside the penalty area could have taken the lead with just four minutes played. It was Tamir Cohen who wriggled free following Sam Ricketts' header but just as he looked set to pull the trigger he was crowded out and Reina blocked his effort from six yards out.
David Ngog, playing up front on his own for the hosts, looked threatening in the first quarter of an hour with his movement through the channels.
The Frenchman forced Jaaskelainen into a decent catch and Ricketts to make a timely interception before heading goalwards from an Acquilani corner. Indeed, Wanderers rearguard, on the back of two clean sheets, looked rather solid especially when a testing inswinging free-kick from Riera asked plenty of questions.
Insua's cross from the left wing also caused concern as it just evaded the outstretched foot of Dirk Kuyt, who would have surely scored if he made any connection.
Owen Coyle's side came within a goal-line clearance of taking the lead in the next attack through a solo effort from the in-form Chung-Yong Lee.
The South Korean winger took on the entire Liverpool defence having picked the ball up on half-way, but just as he rounded goalkeeper Reina, Sotirios Kyrgiakos retreated to make a vital sliding interception.
The only time Wanderers defence was found wanting in the first half was when the home team took the lead on 37 minutes.
It was a well worked move from right to left which resulted in Insua crossing for Acquilani, who nodded back into the path of Kuyt. The Dutchman was unmarked four yards out and despite the best efforts of Jaaskelainen and Cahill, he bundled the ball into the back of net.
Wanderers response to going a goal behind was encouraging as in the minutes leading up to the break, Matt Taylor twice came close with headed efforts, the second one striking the side-netting.
There was also a controversial penalty claim involving Chung-Yong Lee, who took a tumble under an Insua challenge. Instead of blowing for a spot-kick, Steve Bennett booked the winger. However replays suggested that it was a harsh decision.
It took until seven minutes after the restart for the second half to come to live and when it did, Ngog missed a sitter from just four yards out.
Gary Cahill's slip on halfway resulted in a lightning quick counter-attack from Liverpool as Riera galloped down the left touchline. The Spaniard's low cross was seized upon by Gerrard, who brought a fabulous save out of Jaaskelainen, and as the rebound landed at Ngog's feet, he fluffed his lines by hitting the angle of post and crossbar.
Ricardo Gardner was introduced by Owen Coyle on the hour mark as Tamir Cohen made way in a like-for-like change in the centre of midfield.
Gerrard brought another fine stop out of Jaaskelainen before Vladimir Weiss was given 25 minutes of action in his second appearance since joining on loan from Manchester City.
But Liverpool doubled their lead shortly after the winger's introduction with a goal that certainly falls in the fortuitous category.
After a half-cleared corner, Insua struck a speculative drive from outside the area that not only took a wicked deflection off Kevin Davies but also nutmegged Steinsson before creeping into the corner of the net. Jaaskelainen had no chance.
Weiss struck a 25-yard free-kick over the bar and Cahill was unlucky not to latch on to Gardner's set-piece as Bolton's belief didn't waiver.
But Liverpool held firm for the win restricting the Whites to no further opportunities.
Indeed, the margin of the victory could have been extended further before the final whistle as Lucas headed Gerrard's free-kick over from under the crossbar and substitute Rodriguez came within a whisker of converting from point-blank range.
Bolton: Jaaskelainen, Ricketts, Cahill, Knight, Steinsson, Cohen (Gardner 60), Muamba (Elmander 77), Mark Davies, Taylor (Weiss 66), Chung-Yong, Kevin Davies (Subs: Robinson, Al Habsi, O'Brien, Wilshere)
Liverpool: Reina, Acquilani ( Lucas 65), Gerrard, Riera (Rodriguez 73), Kyrgiakos, Kuyt, Mascherano, Insua, Carragher, Ngog (Babel 85), Skrtel (Subs: Cavalieri, Agger, Darby, Pacheco)