Manager Michael Appleton brought in
10 new players on Thursday
on short-term contracts and completed four loan signings in time for Saturday's League One opener.
And Appleton's team of 11 debutants looked as if they had been playing together for years as they took a deserved lead into the break.
McLeod could have increased their lead but shinned over from close range before the break, before he was denied by Jalal with only the goalkeeper to beat.
Pompey tired as the game wore on and Grabban should have done better when he latched onto keeper Andersen's parry from Thomas's shot.
But Grabban fired over and later saw an effort superbly tipped over the bar, before Barnard headed home a cross from Simon Francis.
Pompey pressed late on and Ashley Harris saw his effort crash back off the inside of Jalal's post as the game ended level.
Views from the dressing rooms
Portsmouth manager Michael Appleton tells BBC Radio Solent:
"I thought in the first half we were outstanding.
"It was as if we almost put too much energy into the first half an hour or so.
"That was the first opportunity today for the new players to meet, they've just literally walked into the dressing room, introduced themselves to the players and just got on with it."
Bournemouth manager Paul Groves talks to BBC Radio Solent:
"We knew it was going to be a difficult day with (Pompey) being able to sign players and from the atmosphere that the fans set we knew it would be tough out there.
"Top goalkeepers all make mistakes but it's how they respond and recover from that.
"If you take three strikers out of anyone's squad, it leaves a bit of a hole. I felt with Lee (Barnard) that he is good quality and a good character. He's proven at this level and he fared well in the game.
"I think we need to concentrate on what we've got in respect of trying to build a team."
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