Rochdale boss Paul Simpson took the match ball home after scoring three goals and having a hand in the other two as his side triumphed at the Racecourse Ground.
Wrexham manager Denis Smith said after the match: "His players deserved to win," and described the game as a 'freak result'.
But Simpson said: "I don't know what he means by freak result. We'll take it and we're absolutely delighted. To score five goals we must have done something right."
Smith added: "They're not going to score five every week playing like that. The only thing Rochdale are good at are set-pieces."
Steve Thomas shot Wrexham into the lead, firing home from the edge of the area after Carlos Edwards crossed from the right.
Rochdale stormed back with three goals in seven minutes. Simpson lofted a right-wing free-kick to the back post where Lee McEvilly hooked it into the net.
The Rochdale boss then took another free kick that dipped from the same spot and went straight in.
Gareth Griffiths added the third goal from a Simpson corner that found him unmarked at the near post for an easy tap-in.
Andy Morrell pulled a goal back for Wrexham when he lobbed the ball over keeper Neil Edwards.
Simpson restored his side's two-goal lead this time from the penalty spot after Dennis Lawrence was adjudged to have fouled McEvilly.
Finally he wrapped it up with another penalty when McEvilly was toppled again - this time by Shaun Pejic.
Wrexham were far from out of it but were unlucky with Lee Trundle twice hitting the post and Morrell heading against the crossbar.
Rochdale keeper Edwards was often at full stretch and was at his best with an excellent tip away from Hector Sam as well as making a point-blank save from Shaun Holmes when Trundle's shot came back off the woodwork