McGeehan’s second-half goal ended a winless December for the visitors and consigned Terry McPhillips’ side to back-to-back league defeats.
The visitors were dangerous on the counter-attack, with Brad Potts setting up Mamadou Thiam but he failed to make a clean connection.
Blackpool’s brightest first-half moment came when John O’Sullivan forced Adam Davies to save at his near post.
Dimitri Cavare then found Kieffer Moore unmarked at the back post but the Barnsley striker could only direct his header straight at goalkeeper Mark Howard.
The Reds started the second period on the front foot as former Blackpool man Potts intercepted Jordan Thompson’s back-pass and dragged a shot wide of goal.
Yet Potts made amends shortly afterwards by setting up McGeehan for a simple header at the back post.
Cauley Woodrow’s half-volley flashed narrowly wide and Moore tested Howard in stoppage time as Barnsley comfortably held out for victory.