The south-coast side started brightly, despite giving five players their first starts for the club this season.
But Pools broke the deadlock after 18 minutes, when Jack Baldwin met Evan Horwood's searching free-kick into the box with a stunning flicked header beyond Pompey keeper Simon Eastwood.
The visitors extended their lead after 52 minutes when James Poole raced on to a clearance from the back and rifled home.
Pompey caretaker boss Guy Whittingham made a triple substitution after 63 minutes, introducing Ashley Harris and two more debutants, Yassin Moutaouakil and Frankie Sutherland.
They snatched a lifeline just four minutes later, when debutant Jed Wallace was teed up by James Keene and finished coolly from the right-hand side of the six-yard box.
But second-from-bottom Pompey saw their hopes of a point dashed by Greg Rutherford, who slotted in Jonathan Franks' through-ball in the fourth minute of stoppage time.
