Jay Rich-Baghuelou, Colby Fleetwood and Michael Nottingham put Stanley 3-0 in front at halftime.
John O'Sullivan restored the visitors two-goal advantage and although Rudoni added a second to again make it a ones goal game, it wasn't enough to save the hosts.
Story of the match
Wimbledon had their first chance on 16 minutes as Luke McCormack found a loose ball and slipped it to Dylan Adjei-Hersey, whose shot was easily dealt with by Liam Isherwood.
Two minutes later, Stanley were in front. Rich-Baghuelou was given space to line up a shot that beat Dons goalkeeper Nik Tzanev from distance.
The hosts nearly equalised on the half-hour mark as neat play ended when Assad forced Isherwood into a brilliant save down the right.
Accrington Stanley doubled their lead when a low ball from the left wasn't dealt with properly and it deflected into the path of Bishop as he turned and fired past Tzanev from eight yards out.
It was three right before halftime. Nottingham heading home from a corner, finding the top corner of the net and it looked as though Wimbledon's fate was sealed.
The Dons fought back and were on the scoresheet as Dapo Mebude made his way into the box and setting up Assal for a simple tap-in.
Almost instantly, the hosts cut the lead to 3-2 as a free-kick was sent into the area where an unmarked Rudoni was on hand to head home.
O'Sullivan restored Stanley's two-goal as he got on the end of Sean McConville's cross and while Rudoni responded with his second of the afternoon, it wasn't enough to prevent the Dons from dropping into the fourth tier.
Man of the match: Jack Rudoni
The Wimbledon midfielder was electric, lighting up a dull encounter with two superbly taken goals. Despite the Dons being relegated, Rudoni provided a glimpse of his talents that could carry the Londoners back to League One.