It was earned thanks to a Grant Holt goal after just 17 minutes.
Holt found the target with an angled right-foot shot after John Thompson flicked on a corner by Sam Clingan, but Tranmere looked suspect in defence at the time.
Holt should have netted in the fourth minute following a poor clearance by home keeper Steve Wilson, but his lob towards the empty net went wide of the right-hand post.
The visitors were unlucky not to double their lead after 55 minutes with a lobbed effort by Nathan Tyson from the corner of the box bouncing agonisingly over the crossbar.
Wes Morgan was immense in central defence for the winners and there were also five-star displays in midfield from Clingan and Gary Holt.
Forest have now gone ninematches without defeat and Holt's goal was his fourth for the club since moving from Rochdale.
Tranmere certainly made Forest fight all the way. The Merseysiders were not without their chances but lacked a cutting edge.
Steve O'Leary volleyed wide early on and just before the break Steve Davies saw an excellent effort deflected inches wide.
After the break Steve Jennings headed just wide and in injury time Ian Sharps volleyed over.
It was a sixth home defeat for Tranmere and they are not safe in the division just yet.