Blades striker Conor Sammon came closest to a first-half goal, shooting on the turn and forcing a fantastic one-handed stop from Colin Doyle.
Chances were few and far between for Blackpool, though sub Uche Ikpeazu scooped over from just outside the box.
The visitors were denied all three points late on when Jamal Campbell-Ryce's curling effort was parried away.
Blackpool have now conceded only one goal in their last five home games and are two points clear of the drop-zone.
Sheffield United moved to within a point of the play-off places after a hard-fought draw at lowly Blackpool.