In front of their lowest league attendance of the season, Trond Andersen's first league goal of the season settled a scrappy match of few clear cut chances. He thumped in a half-volley from Alex Tapp's corner in first-half injury time.
Wimbledon only really threatened from corners. Neil Shipperley came closest to adding a second when he met another Tapp corner, but keeper Aleks Kolinko saved well just after the restart.
Palace boss Trevor Francis described his side's performance as "good up to the last 20 yards" as by his own admission Palace had most of the ball, dominated midfield but the standard of crossing was poor.
The Eagles chances were limited, Dougie Freedman was sent through in the third minute by Darren Powell but Kelvin Davis came out and blocked his shot.
Their other chances all came once they were behind. Danny Butterfield tested Davis with a full blooded drive from the edge of the box. Then Freedman's clever pass set up Tommy Black but again Davis blocked the shot.
Freedman's close-range shot was also saved with ten minutes left and the same player put a header wide near the end.
Defeat leaves Crystal Palace 13 points adrift of the play-offs while Wimbledon edged closer with this vital victory.
Manager Stuart Murdoch commented that his team "would be there if anyone slipped up."
He added: "It was not pretty but pleasing. I have been dying for a scrappy 1-0 win all season."
Palace boss Trevor Francis bemoaned his sides continued injury problems and how it has ruined his side's play-off chances.
Their growing injury list was not helped by top scorer Andrew Johnson's torn hamstring in the first half and he will be out for up to six weeks.
Francis did single out Jamie Smith for praise, who having been out for a year with injury and with just a 70-minute reserve outing behind him, was forced to play.