Head coach Danny Cowley made it three wins out of three since taking over the Fratton Park hot seat from Kenny Jackett last month.
Ryan Williams and Ronan Curtis were on target in the first half for the Blues before Jake Beesley notched a consolation for the Dale in stoppage-time.
As a result, Pompey stay fifth in the League One table.
And the result delighted Eisner ahead of the Blues' trip to struggling Wigan on Easter Monday.
Eisner wrote on Twitter: ‘Another important 3 points! Quick turnaround for another match Monday. Happy Easter everybody!!!!! #pup @Pompey
Chairman Michael Eisner tweeted: ‘9 points in the last 3 matches #Pompey.’