Manager Guy Whittingham had demanded pride and passion from his Pompey players after the previous week's miserable 4-2 defeat at York City - and got it in some style.
Jed Wallace got the south-coast club off to a fine start, scoring with a rasping 24th minute left-foot drive which set up a first win in three games.
Portsmouth ought to have made more of their first half dominance, but wrapped up the points with two goals in a 15-minute spell after the break.
Rochdale's defence was twice undone in carbon-copy fashion as N'Gala climbed highest in the six-yard box on two occasions to head home right-wing corners from Ricky Holmes past the despairing Josh Lillis.
Rochdale twice went close in the final stages - substitute Graham Cummins hitting the Portsmouth upright before debutant goalkeeper Trevor Carson made two fine saves at the end.