Ian Henderson and Peter Vincenti scored for Dale after the break, adding to Matt Lund's first-half header. The win saw Keith Hill's men bolster their bid for automatic promotion, while Pompey's problems at the foot of the table intensified.
The visitors started brightly enough with Bondz N'Gala having a header cleared off the line early on. But once Lund headed Dale ahead from close range in the 16th minute, the home side were firmly in control.
George Donnelly fired into the side-netting and Lund headed Joe Rafferty's cross narrowly wide after the interval as Dale pushed for a second. It arrived when Henderson capitalised on hesitancy in the Pompey backline, racing through to collect goalkeeper Josh Lillis' punt upfield and slamming a low drive wide of Trevor Carson in the 59th minute.
Vincenti headed home Matt Done's corner four minutes later to make the result safe and extend Dale's stay at the top of the table.