It was a frustrating afternoon for Tranmere, who dominated for much of the time but found little going right in front of goal and their play-off hopes are now hanging by a thread.
Rovers were dominant for most of the first half and they were unlucky when Chris Greenacre had a 20th minute goal ruled out for offside.
Ian Moore brought a couple of good saves from Paul Smith and Paul McLaren fired just wide following a corner.
Forest went ahead totally against the run of play in the 34th minute following a long ball out at defence by Chris Cohen.
Nathan Tyson got the better of Antony Kay and then rounded keeper Danny Coyne to score his eighth goal of the season.
Ian Goodison flashed a header inches wide for Tranmere ahead of the break and a Chris Shuker header was saved soon after half-time.
The visitors doubled their lead in the 51st minute. Wes Morgan headed his first of the season from a Cohen cross following a corner played short.
Tranmere sent on Steve Davies and Craig Curran to try to liven things up, but it just got more and more frustrating and both Shane Sherriff and Steve Jennings collected unnecessary cautions.
Greenacre saw a late effort deflected for a corner and Moore headed just wide.
Tyson could have had a third for Forest but missed the target by inches after an excellent run through.