Portsmouth took the lead after just 80 seconds when Matthew Taylor snuck in past a static Wanderers back line, but the Lancashire men made sure their winning run was stretched to five as Abdoulaye Faye, Ivan Campo and Nicolas Anelka all weighed in with goals.
Barely a minute of the game had gone when Pompey silenced the home crowd with the opening goal. Following a throw on the right, Manuel Fernandes and Andy Cole combined to slip the ball behind Faye, allowing Taylor to go round Jussi Jaaskelainen to score his sixth, and probably most simple, goal of the season.
Bolton weathered the storm which followed, and could have had an equaliser on 21 minutes when Kevin Nolan and Kevin Davies both went close within a minute of each other.
Nolan's bouncing effort was flicked over the bar by Pompey defender Linvoy Primus and, when the corner broke to Davies at the far post, the former Southampton man should have gone closer with his volley.
Bolton drew level when David James failed to collect Gary Speed's corner on the right, leaving Faye clear to head home from six yards out.
Then, after penning the visitors in their own half for the next nine minutes, the Reebok men took the lead when Tal Ben-Haim's cross was headed goalwards by Davies and, although James did well to keep the ball out, he could only palm it into the path of Campo who did well to head the ball home.
Bolton could have had a third in the 55th minute when Davies played Nolan in on goal, only for Pompey keeper James to block well with his legs.
But the killer goal wasn't long in arriving, Davies sending a dangerous ball into the box that was taken out of James' grasp by Sol Campbell's touch and turned in at the far post by Anelka.
Cole grabbed a consolation goal for the visitors in the dying seconds, and the four minutes of added time provided brief hope of a late comeback, but the Reebok rearguard held firm to further cement their European credentials.