Despite signing 10 players in the days leading up to the game, cash-strapped Pompey rapidly formed a cohesive unit.
Bournemouth came closest to netting in the early stages when Wes Thomas stormed goalwards after a terrific one-two with Marc Pugh, but poked his effort against the foot of the post after six minutes.
Portsmouth fans finally had a huge slice of good fortune to celebrate in the 18th minute when Izale McLeod hit a tame, low shot from 25 yards out, which squirmed through the legs of Bournemouth goalkeeper Shwan Jalal.
The Cherries improved dramatically after the break and Lee Barnard rose highest to nod home Simon Francis's cross to haul the visitors level after 73 minutes.
But Bournemouth could not overcome resolute Pompey, who came within millimetres of snatching three points when a last-minute strike from substitute Ashley Harris cannoned off the inside of Jalal's post.