The Cherries made it through to the second round of the Capital One Cup with a dominant performance and a second half goal from Eunan O’Kane.
The hosts had been much the better team before O’Kane’s strike eight minutes after the restart, but got the goal their efforts deserved when the midfielder calmly sidefooted the ball past goalkeeper Phil Smith.
While loan signing Andrew Surman had further chances and Tom Craddock tested Ryan Allsop with a looping header, the tie was settled within 90 minutes.
The draw for the second round will be made live on Sky Sports at 12.30pm on Thursday, with the games to be played the week commencing 26th August.
And The Cherries could be drawn against one of the Premier League teams not involved in the Champions League or Europa League this season.
Eddie Howe made four changes to his starting line-up, which included a return for Tommy Elphick and a debut for Ian Harte.
Although the visitors spent most of the opening 45 minutes in their own half, Patrick Agyemang saw his ambitious volley from 30 yards bounce narrowly wide.
However, the Cherries enjoyed most of the early possession and were playing with real pace and purpose, but couldn’t cause their opponents any problems in the final third.
That was until O’Kane picked out Simon Francis with an incisive pass and the full back sent in a dangerous cross, which only just eluded Wes Thomas at the back post.
Thomas then sent in a header and Surman had a half volley blocked as the Cherries increased the pressure.
And Pompey goalkeeper Smith had to make two full stretch saves in injury time to keep the scores level.
First, he denied Surman and then Ryan Fraser had a curling effort pushed away by the Pompey number one.
But he could do nothing to stop O’Kane scoring the opener when he collected Fraser’s deflected shot and slotted beyond Smith.
It was clear to see what the goal meant to O’Kane, who missed most of pre-season with a thigh injury, as he celebrated in front of the Steve Fletcher stand.
The hosts went on to create a number of chances in the final 30 minutes and Surman was unfortunate to see a couple of long range efforts fly narrowly wide of the post.
Substitute Charlie Daniels, playing on the left hand side of midfield, had a shot saved at the near post as he tried to ensure a more comfortable win for the Cherries.
Cherries: Allsop, Francis, Elphick, Cook, Harte, O’Kane, Hughes, Surman (Arter 83), McDermott, Fraser (MacDonald 88), Thomas (Daniels 72).
Unused substitutes: Flahavan, Addison, Matthews, Stockley.
Booked: Elphick, Hughes
Goal: O’Kane (53)
Portsmouth: Smith, Devera, N’Gala, Bradley, Butler (Ferry 64), Wallace (Barcham 71), Padovani, East, Holmes, Agyemang (Bird 71), Craddock.
Unused substitutes: Sullivan, Moutaouakil, Connolly, Harris.
Booked: East, Butler, Holmes, Wallace
Attendance: 7,620 (including 1,354 Portsmouth supporters)