Pompey had to settle for a point after 10-man Blackpool were able to hold on for a draw at Bloomfield Road.
John Mousinho's men improved as the contest progressed and received a numerical advantage when Jordan Rhodes was dismissed just before the break.
They struck the post on three occasions in their search for a winner, but were ultimately left frustrated.
The goalless stalemate means that the Blues have a five-point advantage at the top of the standings.