AFC kept their first clean sheet since early September on their return to action after a weather-enforced three-week lay-off.
READ MORE: Squires Gate 3 AFC Liverpool 2
After an even first 15 minutes on Stockport’s all-weather surface, the home side took control and Callum Kirkland made good saves from long-range efforts.
The visitors gave the ball away too often and were grateful for the half-time whistle.
However, they were much improved in the second half, though defences were on top.
The introduction of Kit Gregory provided a much-needed spark and his one-two with Ben Duffield resulted in AFC’s best chance, a shot which was saved for a corner.
Stockport were the better side but they didn’t do enough in front of goal either to merit three points.
Defender Alex Caunce was AFC’s man of the match as he chased back to thwart Stockport’s pacy wingers.
It means AFC avoided a third successive defeat and stand eighth in the Hallmark Security League first division.
They head to Prestwich Heys on Tuesday in the quarter-finals of the LWC Drinks First Division Cup.
Blackpool: Kirkland, Nay, Baird, Caunce, Betteridge, McKenna, Cassidy, Fishwick, Dawqson, Hargreaves, Duffield; subs: Pickering, Bishop, Williams, Gregory.