Daggers took the lead after two minutes with a wonderful move involving Andre Boucaud, Billy Bingham and Christian Doidge.
The ball eventually dropped to Cureton and he headed in, despite Barry Fuller’s best efforts on the line.
Dons tried to respond and should have equalised in the 24th minute when Alfie Potter crossed in from the left, but Craig Tanner headed wide from close range.
It remained 1-0 at half time, but 13 minutes after the break Daggers doubled their lead when Scott Doe met Andre Boucaud’s corner and headed in at the back post.
Although Wimbledon looked to reduce the arrears in the 71st minute Wayne Burnett’s team made the points safe.
Luke Howell’s long pass found Cureton and he fired over Ross Worner to put the hosts three up.
There was more to come for Daggers and Cureton, though, as Alex Jakubiak teed up the 39-year-old three minutes later and he curled into the top corner for his hat-trick.