Carlisle overcame an early setback to deservedly claim their first win of the month in front of a set of 521 very vocal and happy travelling fans.
The hosts took the lead with just 61 seconds on the clock when Meppen-Walter had his pocket picked by Azeez deep inside his own half. Sean Rigg called for it and his cross to the far post had Akinfenwa interested. He arrived unchallenged to tap it in from close range.
The Dons went close again moments later when Oshilaja flicked a near post corner into the mix. Goodman took a touch but he couldn't keep his volley down. Another lobbed free kick caused problems as the Dons stayed forward and Grainger had to block an Azeez shot at source as he tried to finish it off.
A long ball forward brought an unexpected opening for Reeves, as he nipped in front of Griffith in the centre circle, and Gillespie had to readjust as a dipping volley threatened to creep under his bar.
United were back on level terms just after the quarter hour when Dempsey sent a curling free kick to the near post. Sean O'Hanlon muscled his way through and he left Shea with no chance as he thumped his header into the top corner.
The Cumbrians looked a different side and a Grainger long throw had to be blocked twice as Rigg and Sweeney tried to get the vital touch. Sweeney was close again when the corner came in as he raced across the back line and glanced it into a ruck of bodies.
The crossbar saved United as Wimbledon tried to reassert their authority when Akinfenwa twisted to nod a looping header from the edge of the box. Gillespie was beatean, and relieved to see it bobble wide as Sean Rigg scuffed the rebound wide of the mark.
The hosts stayed forward and Akinfenwa brought the best out of Gillespie when the big striker got onto the end of a cross from Azeez. The downward header was going in until a firm hand pushed it away.
United could have grabbed the lead just before the break when Dempsey slid the ball through the back line for Potts to chase. He set himself for the first time shot but Shea dived low to complete a fine save and deny the midfielder his moment of glory.
The sides cancelled each other out through the tentative closing stages of the half but the visitors thought they'd notched when Potts fed Grainger on the overlap. He took it wide and was unlucky not to register as his crisp shot, from a tight angle, whistled just past the upright.
Things stayed tight after the break but Fuller took things into his own hands when he sprinted clear from inside his own half. Akinfenwa was there for the cross but he lost his bearings and sent his header into the side netting.
United hit on the break to get themselves ahead just before the hour when Potts and Dempsey combined in midfield. Right back Matt Young popped up in support and his cross was perfect for the rising Steven Rigg to finish off with the cleanest of headed strikes.
High balls into the box failed to trouble the Carlisle defence but the Cumbrians somehow survived a late goalmouth scramble when an inswinging corner was twice cleared off the line. Akinfenwa was first to be denied, and Francomb was next to be left with his head in his hands as he pulled his volley wide.
But it was stopper Mark Gillespie who earned late hero status when he kept his eye on a fizzed cross as it skipped across his six yard line. Barry Fuller pulled the trigger and the alert keeper spread himself to make what was a world class and match winning save.
Francomb curled another shot wide as the Dons kept the intensity level high and Akinfenwa popped a header wide when it looked easier to score.
Carlisle wrapped up their points deep into time added on when Dempsey burst out of his own half. His shot was parried but substitute David Amoo was on hand to place it into the back of the net with the coolest of finishes.
And it could have been even better when another late counter attack left five yellow shirts unmarked inside the box. Striker Mark Beck was off balance as he hung out a leg and sent it at Shea as he tried to pick a spot in the far corner.
Wimbledon - Akinfenwa (2)
United - O'Hanlon (16), Rigg (56), Amoo (90)
United - Grainger (71), Young (86)
AFC Wimbledon - Shea, Fuller, Kennedy, Reeves (Nightingale 89), Oshilaja, Goodman, Sean Rigg (Potter 65), Bulman, Azeez (Connolly 65), Akinfenwa, Francomb. Subs - McDonnell, Harrison, Moore, Pell.
Carlisle United - Gillespie, Young, O'Hanlon, Archibald-Henville, Grainger, Meppen-Walter, Griffith, Potts (Amoo 83), Dempsey, Sweeney (Beck 90), Steven Rigg (Asamoah 74). Subs - Hanford, Thirlwell, Gillies, Brough.
Referee - Mr Mike Bull
Attendance - 4,186 (521 away fans)