The visitors had enjoyed slightly the better of the opening exchanges before the first real strike on goal from Blackpool's Keith Southern after three minutes.
A minute later Euell broke the deadlock and it was too easy for the former Charlton striker, who placed his header from six yards out after a good cross from Stephen Crainey on the left.
Two minutes later the visitors were almost back on level terms after good work from Aaron McLean to smuggle the ball through to the prolific Craig Mackail-Smith, but the striker saw his shot turned away by Paul Rachubka in the Blackpool goal.
Blackpool doubled their lead in the 11th minute through a piece of Magic from Bouazza for his first goal for the Seasiders.
The winger looked short of options tight to the byline but he knocked the ball past Russell Martin and beat the Peterborough man to pace before hammering a beautiful drive past Lewis from the tightest of angles for a goal that never looked possible.
Blackpool could have extended their lead through Brett Ormerod, who had a couple of decent opportunities after being put through by the impressive Euell.
But it was Peterborough who enjoyed the better chances after an injury to Neal Eardley disrupted the home side's rhythm.
The best chance came five minutes into the second half when George Boyd found McLean, whose header looked bound for the goal until Blackpool's Rob Edwards came across to clear his lines.