In an all-NPL third round affair, quickfire second half goals from Adam Boyes and Dale Hopson were enough for the Seasiders to reach the Last-32 of the competition.
Their victory came despite the absence in the dugout of manager Curtis Woodhouse, who missed the game through illness.
They will visit Farsley Celtic of the National League North in the next round, after they defeated Chester on penalties.
Guiseley, the only other NPL side left in the competition, were beaten 1-0 at home by National League FC Halifax Town.
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