Bondz 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.
Dale's defence was twice undone in carbon-copy fashion as N'Gala climbed highest in the six-yard box to head home right-wing corners from Ricky Holmes past the despairing Josh Lillis.
Midfielder Jed Wallace had given the home side a deserved half-time lead with his second goal in as many matches.
The visitors went close in the final stages - substitute Graham Cummins hitting the Portsmouth upright before debutant goalkeeper Trevor Carson made two fine saves.
Hill said: "This has been a big learning curve for the players and about what we have to do. Portsmouth gave us immense respect and put us under a lot of pressure.
"But I cannot legislate for the mistakes. We have not become a bad side overnight. We are a good side with good players, but individual errors cost us.
"All season we've been brilliant at defending set plays, but we didn't mark today and conceded two headed goals inside the six yard box.
"We can definitely recover from this and I'm sure we can go off on another run, but what we can't make is mistakes like that and expect to win any game."