Wanderers looked low on confidence early on but when Davies latched onto namesake Kevin's through-ball to break the deadlock in the 41st minute the pressure was eased.
Neither side really created many chances of note but after two successive Premier League defeats a first victory of the season came as a welcome relief for Gary Megson's side.
Bolton's recent record against Tranmere was not good with just three wins in 12 previous encounters and there was a sense early on that an upset could be on the cards.
Wanderers felt the tension too as even the usually dependable Matt Taylor and Kevin Davies failed to properly test goalkeeper Luke Daniels when the ball dropped to them on separate occasions in the penalty area.
Jlloyd Samuel's foul on Terry Gornell in the right corner allowed Alan Mahon to whip in a vicious free-kick which Gary Cahill did well to head clear as Tranmere matched their more illustrious opponents.
Midway through the half Megson made a tactical switch and pushed Kevin Davies up alongside £10million striker Johan Elmander, who has now not scored in 21 matches since December 13.
Taylor came closest to scoring in the 30th minute when right-back Sam Ricketts got to the touchline and crossed to the far post but his team-mate just headed over.
Tranmere were crying out for the sort of creativity their manager John Barnes regularly provided in his playing days but as the half wore on Bolton gradually began to grind down their hosts.
Their resistance was broken in the 41st minute when Kevin Davies played a neat ball through the inside-right channel and his namesake Mark's shot somehow went through goalkeeper Daniels' clutches.
The goal was Bolton's first of the season and it gave them a platform in the second half to get a firmer grip on the game.
Mark Davies was too clever for Aaron Cresswell in the centre-circle and the Tranmere left-back was booked for bringing down the midfielder.
Sean Davis' deflected shot off Welsh had Daniels frantically backpedalling to tip over as Bolton's dominance began to grow.
Goalscorer Mark Davies then almost repaid the favour for striker Kevin on the hour with a cross to the far post but although the Wanderers captain was at full-stretch he could not get a touch.
Megson replaced Mark Davies with Lee Chung-Yong, a decision the midfielder appeared to disagree with as he headed straight down the tunnel, while the appearance of former Bolton striker Michael Ricketts as a Tranmere substitute brought a chorus of boss from the visiting fans.
Elmander should have made the game safe in the 77th minute but failed to beat Daniels from five yards with a header from Taylor's dinked cross, the ball somehow deflecting behind.
The Swede also forced a low save from the goalkeeper with a long-range strike late on as his goal drought continued.