The home side thought they had taken the lead when Connor Jennings was put through on goal before finishing well, but the assistant linesman had his flag up for offside.
Next it was Andrew Cook who fired a drive from 25 yards out, but Lions ‘keeper Dan Atkinson saved the effort and was then able to clear the rebound with his feet.
Guiseley were being compact in defence with Luke Porritt causing problems, but there were few chances being created by the visitors.
Tranmere took the lead just before half-time when James Norwood was found in the area and, on the angle, he produced a smart finish that left Atkinson helpless.
The second half started with Guiseley trying to initiate attacks, but Rovers’ defence was coping well with what the away side tried to do.
Guiseley had a decent chance when Javan Vidal controlled a pass well and saw his effort saved by Scott Davies.
But the away side could not create anymore chances meaning the Nethermoor side stay bottom on zero points.
Guiseley return to action on Saturday at home to fourth-bottom Braintree.
North Ferriby United dropped to 20th after a 1-0 loss at home to Barrow who moved 10th. Ferriby are back in action on Saturday at 13th-placed Eastleigh.
In National League North, Jack Emmett’s forceful finish gave Harrogate Town a colossal 1-0 win in the Yorkshire derby at FC Halifax Town.
Emmett fired home the only goal of the game midway through the second half to stretch Town’s unbeaten start to the 2016-17 campaign to seven matches.
But despite claiming the three points, Simon Weaver’s men dropped one place to third as Class of 92-owned Salford City went above them on goal difference.
Salford beat Curzon Ashton 2-0 to better Town’s goal difference by one and move into second place behind AFC Fylde – Town’s conquerors in the play-offs last season.
Emmett’s goal brought to life a dull encounter at the Shay Stadium, which had seen the teams cancel each other out in the first 45 minutes.
Town lost Warren Burrell through injury in the 38th minute of an otherwise uneventful half.
The second began in the same vein, too, until Emmett found time and space on the right wing and crashed home a shot off the underside of the crossbar
Halifax, who were in fifth place prior to the match and are fancied for an immediate return to the National Premier League, could not respond and targetman Tom Denton headed a late chance straight at Peter Crook.
The Shaymen are back in action next Saturday at 14th-placed Telford.
Leaders Fylde were 4-1 winners at Bradford Park Avenue for whom a strike from Chris Sharp strike was in vain.
Avenue sit 18th and return to action next Saturday at ninth-placed Brackley Town.
Harrogate Town host 13th-placed Curzon Ashton the same afternoon.