Stevenage almost broke the deadlock inside 13 minutes when Jimmy Smith's header bounced awkwardly off the floor in front of goal, but Rovers' goalkeeper Jason Mooney got his fingers to it.
Tranmere striker Ryan Lowe thought he had won a penalty after 18 minutes when Stevenage captain Jon Ashton brought him down inside the box, but the referee deemed the challenge fair.
Home forward Jean-Louis Akpa Akpro rattled the crossbar in the 33rd minute with a delightful curling-shot after working himself some space inside the penalty area.
Stevenage winger Luke Freeman smashed in a low shot five minutes later after cutting back inside the Tranmere defence, but could only find the side-netting.
Atkinson rifled in a testing long-range shot for the hosts five minutes before the break, but Stevenage keeper Chris Day parried the ball to safety.
Atkinson sent Day scrambling again two minutes later, but the Huddersfield loanee struck the ball narrowly wide.
Tranmere defender Evan Horwood smashed a shot against Day's right-hand post in the 59th minute with a well-struck attempt from 25 yards.