A stunner from Danny Philliskirk, picking out the corner from 20 yards, got the ball rolling and he turned provider for Cullen minutes after the break.
Cullen completed the victory after racing onto a pass from Armand Gnanuillet and calmly finishing the scoring on 66 minutes.
It was a well-fought opening to proceedings at Victory Park and Blackpool mustered the first opening when Philliskirk dragged wide.
The next opening fell to Sean Longstaff but the midfielder’s effort was kept out by the feet of Matt Urwin.
It was nearing the half-hour mark when Ben Williams made his first serious save, as he had to be at his best to tip over Terry Gornell’s effort.
At the other end Peter Hartley, who was left unmarked from Nick Anderton’s corner, had an effort cleared from almost on the goal line.
The opening goal had been coming and finally arrived on 34 minutes, as Philliskirk fired a brilliant effort into the top corner from all of 20 yards.
Seconds later it should have been two, as Gnanduillet ghosted into the area but, when he should have squared for Cullen, he was eventually crowded out.
After the break the visitors quickly made it two, as Anderton’s cross was flicked into Cullen’s path by Philliskirk and the striker was coolness personified when tucking his effort beyond Urwin.
The closest Chorley came to scoring came in the 48th minute, but after Gornell’s header had come off the inside of the post, Williams reacted to thwart Marcus Carver.
From the resulting corner Williams again excelled, getting down low to keep out Adam Roscoe.
Blackpool’s third goal killed it as a contest, as Cullen raced onto a chested pass from Gnanduillet, gave the goalkeeper the eyes and picked out the opposite top corner.
That was the striker’s final contribution, as he was replaced by Caleb Richards, with Nathan Delfouneso and Ollie Turton pushing up a position.
With time running our Urwin made another impressive to deny Andy Taylor.
Blackpool: Williams (Mafoumbi), Turton (Newton), Taylor, Hartley, Anderton, Trialist, Longstaff (Sumner), Delfouneso (Des Pres), Philliskirk, Cullen (Richards), Gnanduillet.