Nine-goal Dagnall opened Rochdale's account on the stroke of half-time and then created two second-half goals for loan man O'Grady.
Simon Whaley got the other goal before midfielder Nathan Stanton soured the victory when he was sent off for a bad tackle on Bournemouth substitute Marvin Bartley.
"We've produced a number of good results over the time I've been in charge, but this was probably our best bearing in mind the magnitude of the game, with first playing third," beamed Hill.
"I rate Bournemouth as definitely being among the promotion contenders this season. I'm not getting carried away. This is just one result in a very long season but we came with a gameplan and it worked to very good effect."