West Brom halted their run of four away defeats but were still left frustrated after this stalemate at Bloomfield Road.
Boss Valerien Ismael's demand for more composure in front of goal went unheeded as his team missed numerous chances to make up some ground on leading pair Fulham and Bournemouth.
Albion remain in third place but after a 10-game unbeaten start to the season, they have taken only four points and scored two goals from their last five games.
West Brom have lost more ground on the league
Grady Diangana, Alex Mowatt, Connor Townsend and Karlon Grant all failed to take good opening in the first half when Blackpool keeper Dan Grimshaw was kept busy
But Albion had their keeper Sam Johnstone to thank for keeping them level at the break with a double save from Gary Madine and Keshi Anderson.