Jake McCarthy put the Cherries in front mid-way through their first half, with Brandon Goodship adding a second just after the break.
Pompey pulled a goal back but Ross Embleton’s side finished the stronger of the two teams, and Goodship scored his second of the afternoon to restore the two-goal lead.
Embleton was delighted for his player following the final whistle and felt the result was just rewards for their efforts in recent weeks.
“It was very pleasing for the boys to get their first win. We have had some positive individual and team performances in pre-season and the first few weeks of the season, but it doesn’t always get recognised when you don’t win,” he told afcb.co.uk.
“I think the win will give the boys a bit of a lift and a bit more belief in what we are trying to do.
“What is important to John (Donoghue) and myself as coaches, is that we did it in a manner that we expect and the club are beginning to expect.
With almost a month of the season gone, Embleton added that he was pleased with the progress the youth team have made since his appointment in the summer.
“It can be difficult to get the message across to the boys that they have been doing as well as they have because they hadn’t won before the weekend,” he said.
“After three games they are bottom of the league but that doesn’t tell you the whole story.
“I’ve been really pleased with the way they have taken to me, and the relationship I’ve built up with John and the way we work during the week.
“I think the benefits of that are starting to show through in the performances the boys are putting in.”
Cherries: Collins, Davis, Kaye, West, Buckley, West (Turner, 80), McCarthy, Smith (Butcher, 75), Kirkwood, Roberts, Goodship, Walsh (Blackmore, 60).
With the absence of a Youth Alliance fixture this weekend, the youth team will play an in-house friendly with the under-16s.