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This victory comes after a weekend win at the City Ground against Nottingham Forest, as Owen Coyle's side have at last found their stride after a slow start to the season.
Burnley began brightly with home debutant Steve Thompson firing over the crossbar inside the opening minute.
Blackpool goalkeeper Paul Rachubka made a fine save to parry a Chris McCann free-kick from 20 yards, while central defender Ian Evatt did well to block a goalbound effort from winger Wade Elliott.
Full-back Russell Anderson was close to his first goal for Burnley with a shot that took a deflection and just missed the far post.
Blackpool's only attempt at goal in the opening half arrived after 28 minutes when Evatt headed straight at home goalkeeper Brian Jensen.
Midfielder Kevin McDonald had Burnley's last chance in the opening half but was caught in two minds and shot tamely wide of the near post.
The opening 15 minutes of the second half were more evenly contested, but the deadlock was broken on the hour with a fine left-foot strike from Paterson, as he curled his shot into the far corner of the net from 20 yards.
Five minutes later Clarke Carlisle had an opportunity but fired wide of the target.
Paterson forced another save from Rachubka before Burnley made the game safe with a penalty 16 minutes from time, which was awarded by the assistant referee after central defender Steven Caldwell had been hauled down at a corner.
The resultant spot-kick was converted with relative ease by Alexander to secure the win for Coyle's side.