The victory was as comfortable as the scoreline suggests.
The home side were quickly on the front foot and their good start was rewarded with an early goal from Billy McKenna, whose low drive from the edge of the box found the bottom corner.
Eccleshall were reduced to 10 men after only 20 minutes when the centre-half received a straight red card for bringing down McKenna when clean through on goal.
The points were then all but sealed either side of half-time thanks to goals from Kit Gregory and Alex Taylor.
The latter then converted a penalty to make it four and a fine individual performance from McKenna was capped with a late fifth.
Victory means AFC Blackpool now lie seventh in the table and perfectly poised for a push on the play-off places.
They are at home again on Tuesday evening when they come up against St Helens Town FC (7.45pm kick- off).
AFC Blackpool: Kirkland, Donaghy, Baird, Betteridge, Bishop, Pickering, Hargreaves, McKenna, Gregory, Taylor. Subs: Mottram, Fishwick, Dawson.