The Stags were lucky to be just one down at the break after Blair Sturrock scored on 25 minutes with a low angled drive past Stags goalkeeper Kevin Pressman.
There could have been more for Rochdale with two shots headed off the line while the goalkeeper was absent without leave as another one hit the woodwork.
Mansfield looked much better after half time, but if their approach play had improved their shooting had not, and several times they let Rochdale off the hook with imprecise marksmanship.
Richie Barker put a header over the top of an untenanted goal from a couple of yards out and only he will know how he managed to do this.
Jon Olav Hjelde was given his marching orders after 65 minutes when he appeared to elbow Rochdale's Alan Goodall in the face. After Hjelde had been given marching orders, as often happens, the Stags improved and gave Rochdale a few anxious moments.
But thanks to bad marksmanship, Rochdale held out and Grant Holt managed to get another one seven minutes from time, weaving his way through following a free kick from the left touchline.
All in all, it was a pretty poor day for Mansfield, but they produced a bit of verve late on without collecting the harvest for all their hard work and the odd touch of brilliance.