The home side opened the scoring after just seven minutes, with Reece Smith curling in an effort from distance on the right side - leaving the ball well out of Franco Ravizzoli’s reach.
Things quickly got worse for the Seasiders, as the North Yorkshire outfit swiftly doubled their lead.
At the front post from a Smith corner, Ravizzoli couldn’t deal with a flicked effort towards goal from Warren Burrell, leaving the ball loose on the line for O’Connor to tap in from close-range.
Inside 17 minutes, Harrogate had extended their lead to 3-0. The Sulphurites’ first scorer of the evening added an assist to his collection, slipping through Muldoon - whose side-footed attempt from the edge of the area hit the underside of the crossbar on its way in.
Just before the break, Blackpool were able to pull one back, with James Husband slotting through Hansson - who neatly finished past Belshaw.
Following the restart, Fletcher came close to instantly clawing another back, but was denied by a strong save from the Sulphurites keeper.
Belshaw’s next stop was his most impressive of the game, as he clawed away a header from Horsfall just past the hour mark.
Blackpool were eventually able to beat the 35-year-old once again, with Fletcher finding a way past him.
Despite the Seasiders enjoying a much-improved second half, they were unable to complete a mammoth comeback, with Muldoon securing the progression of the North Yorkshire club with a goal on the break in the 84th minute.
Here’s how the Seasiders performed:
