Tranmere were somewhat lethargic in the opening period, before they stepped up the pace later but were unable to find a way through the Seasiders rearguard.
Indeed, Colin Hendry's men could have snatched it in injury time when a goal bound header by John Murphy appeared to be deflected off target by the arm of home defender Mike Jackson, but no penalty was given.
Blackpool had the better of the opening period but Keith Southern had no luck with three good efforts and Simon Grayson flashed a shot just over.
Tranmere should have taken the lead in the 19th minute when Iain Hume burst clear and lobbed the ball over keeper Lee Jones only to see his effort hit the outside of the post.
Tranmere did most of the attacking after the break but Jones saved well from substitute Chris Dagnall, Ryan Taylor put a free-kick into the wall and Jackson headed over.
Then Jones produced the save of the match to tip over another Jackson header in the 69th minute.
As Tranmere searched for a winner Hume headed wide and Dagnall was denied by the legs of the keeper, who earned his side a valuable point.