A Joel Sutton penalty 10 minutes into extra-time ensured that a disciplined performance by the Seasiders sent them into the third round where another away tie awaits them.
Despite a man-to-man marking system and some dubious decisions against both sides, Town’s character shone through to overcome a difficult hurdle.
The hosts started in a positive mood with Philip Dobson blocking an effort from leading scorer Joe Thornton and Craig Palmer clearing up.
Sutton went past two defenders before passing to Craig Hogg, whose lay-off was struck just past goalkeeper Darren Shirt’s left hand post by James Bennett.
An Ash Allanson free kick was cleared only as far as Sutton and his ball in was met by Chris Jenkinson who found the grateful hands of Shirt. The game went from end to end and Thornton, after being fouled by Fleming, hit a 25-yard free kick wide of goal.
Robert Cartwright flicked Jack Briscoe’s pass towards goal where Dobson’s outstretched leg diverted the ball away before Jenkinson made two timely tackles to stop both Thornton and Briscoe as they broke down the right.
The first half had been fairly even but it was Town who started to press in the second and an effort from Sutton clipped off Shirt and cleared the bar.
Tom Fleming was cautioned for what appeared to be a perfectly legitimate challenge and following a free-kick Briscoe sent a 30-yard strike the wrong side of the post.
The nearest either side came to breaking the deadlock was when James Bennett hit the underside of the bar with Craig Hogg putting the rebound over, and Thornton missed the target with a free header.
Athersley skipper Ryan White was booked for pulling back Fleming as Town tried to win the tie in normal time and towards the end Hogg and Bennett had shots charged down while Tom Lee put a good chance over the top as Athersley desperately defended their goal.
In the first period of extra-time Athersley had a good shout for a penalty turned down and after seven minutes had been played they were lucky not to be reduced to 10 men when Briscoe was shown just a yellow card after going straight through Frank Belt leaving the defender requiring extensive treatment on a foot injury.
Three minutes later Ryan Blackburn felled Sutton around the edge of the area with the referee’s assistant signalling that the offence occurred inside the box. With regular penalty taker Belt nursing his injured foot Sutton converted his fourth spot-kick of the campaign.
After the change-round Town kept the pressure on and Hogg had an effort cleared off the line.
With time running out Shirt was sent forward for dead ball kicks and just failed to connect from a free kick but Town saw the game out to obtain a deserved win.