The Merseysiders could not capitalise on their early chances as they slumped to their sixth home defeat of the season.
Forest went ahead against the run of play in the 34th minute following a long clearance by Chris Cohen as Nathan Tyson got the better of Antony Kay and rounded keeper Danny Coyne to net his eighth of the season.
The visitors doubled their lead six minutes into the second-half with Wes Morgan heading in his first of the season from a Cohen cross.
Tranmere tried hard to get back in the picture but Chris Greenacre saw a shot deflected for a corner and Ian Moore headed wide
Sub Kris Commons raced clear in the 80th minute for the visitors but his shot missed the target.