N'Gala's second-half headers 15 minutes apart sealed Pompey's first win in three matches and ended Dale's four-match winning run.
Midfielder Jed Wallace had given the home side a deserved half-time lead with his second goal in as many matches.
Delighted Whittingham said: "There was no better way for us to bounce back after last week's defeat at York. To score three goals and keep a clean sheet was near enough perfect.
"It's a minimum requirement for any football team to go out and work hard and we did that against Rochdale. We played sensibly enough and kept our heads and did the ugly side of football, which we needed to improve on.
"There was a definite lack of desire at York and there was none of that today. It starts at the front where your strikers are chasing men down and spreads through the team.
"Jed Wallace had a great game and got us going with a top goal. He's a confident lad and two goals in successive matches will do him the power of good."
The victory eases the pressure on Whittingham, who this week held crisis talks with Pompey chairman Derek McInnes in the wake of last weekend's 4-2 defeat at struggling York.
Wallace got the south-coast club off to a fine start, scoring with a rasping 24th minute left-foot drive to match his solo strike at Bootham Crescent.
Pompey 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.
Dale'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.
The visitors went close in the final stages - substitute Graham Cummins hitting the Portsmouth upright before debutant goalkeeper Trevor Carson made two fine saves.