Davies volleyed home a gift in the 62nd minute after fatal hesitation in the home defence with keeper Jan Budtz stranded on the edge of the penalty area.
It was Tranmere's first league goal in more than nine hours of play and it gave them their first league win in 10 games.
Tranmere boss Brian Little won the tactical battle hands down as the visitors worked tremendously hard to stop the home side playing before gradually imposing themselves on the game.
Doncaster lacked their usual sparkle and the visitors were first to threaten following a free-kick from Davies in the third minute.
Michael Jackson out jumped everyone to produce a powerful goalbound header from close range but home keeper Budtz reacted instinctively to make a brilliant save.
Tranmere defended superbly when Doncaster tried to apply pressure and centre-back Ian Sharps made a magnificent tackle to prevent Paul Green from scoring in the 22nd minute.
Paul Heffernan fired over the top soon after before Davies headed wide on the stroke of half time.
Tranmere gradually began to get on top after the interval and Doncaster were fortunate when Steve Roberts came to the rescue to clear off the line in the 49th minute after Budtz had been beaten by a header from Delroy Facey.
Facey and Davies went close in quick succession before Tranmere made the breakthrough with Davies' opportunist strike after Doncaster had waited in vain for Budtz to clear a long through ball.
Doncaster never really looked like battling back and Stephen Jennings wrapped up the points in injury time when he raced past Budtz to fire home in fine style after latching on to a defence splitting pass from Chris Greenacre.