The first opportunity fell to the visitors as Jack Cork sliced a shot wide of the mark and from then on it was Blackpool's half.
Charlie Adam came close with a free-kick in the opening five minutes and just moments later Gary Taylor-Fletcher saw an effort come back off the crossbar as the home side looked to break the deadlock.
Sammy Clingan gifted Pool the opener after he brought Ben Burgess to the ground with a soft tackle and summer signing Adam fired home a low strike from the resulting spot-kick.
As Blackpool's confidence grew Coventry found little in reply as the bulk of the chances continued to go Pool's way and, on the stroke of half-time, the home side should have doubled their lead as an excellent cross from Neil Eardley whistled narrowly ahead of the onrushing forwards.
After the break Coleman's side emerged confident but they could not find the edge in the final third. Just before the hour mark, Blackpool showed the way as unsung hero Brett Ormerod floated a cross Burgess' way and the tall frontman charged his header in off the crossbar for the second.
Coventry came close to grabbing one back as a close-range Leon Best strike was cleared off the line but it was Pool who deserved the victory and, just moments later, Taylor-Fletcher slid an easy goal amid a stumbling defence to seal the points and Blackpool's first league win of the season.