Davies netted the only goal of the game at Prenton Park shortly before the half-time interval to give Gary Megson's men something to cheer after two successive league defeats.
The Trotters have suffered two 1-0 losses in the Premier League so far this season, but the former Wolves midfielder ensured there was no repeat against the League One side.
Megson drafted defender Jlloyd Samuel back into the side and it was the former Aston Villa man who carved out the first chance against John Barnes' men after crossing for Johan Elmander to slide the ball wide of the mark.
John Welsh was the first to chance his arm for Rovers but his effort was comfortably saved by keeper Jussi Jaaskelainen from 25 yards.
Alan Mahon flashed two efforts wide of the mark for Tranmere while Elmander stung the palms of keeper Luke Daniels.
But Davies broke the deadlock in the 41st minute while he latched onto a through-ball from namesake Kevin Davies and fired past Daniels from the edge of the box.
Bolton went for the jugular after the break but Fabrice Muamba, Sean Davis and Kevin Davies were all thwarted by a defiant Rovers rearguard.
Elmander should have doubled the lead in the 76th minute for the Trotters when Matt Taylor's header fell into his path, but the Sweden international missed from all of four yards.
Daniels was again on hand to prevent Elmander opening his account for the season in the dying minutes as he tipped a long-range effort around the post.
Ryan Fraughan almost forced the tie into extra-time with the final whistle approaching, but he could only find the side-netting.