Pompey's failure to kill off the game at Fleetwood was manager John Mousinho's only disappointment as he hailed one of the Blues' most important wins of the season.
Their Highbury victory puts them back on track after defeats to Cheltenham and Leyton Orient had seen their lead at the top of League One all but wiped out.
Abu Kamara got the only goal but Pompey couldn't add to their score and had a few nervous moments in the second half.
Mousinho told the club media: 'It always felt like if we could get a win, it would be up there with the most important of the season for us. Coming off the back of a disappointing performance last week and in tough conditions on a difficult pitch, I’m thrilled for the lads and for the fans.
'It was really good football in the first half and then dogged determination in the second to keep the ball out of our net. We were in control before the break, keeping possession against a hard-working side and if we kept at it, we knew that things would open up.
'That happened on a few occasions and there was that bit of quality in the final third, which we’d perhaps been lacking in recent weeks. I can’t demand something like that from Abu every single week, but he has certainly got it in his locker.
'In the second half I didn’t feel the game got away from us, although we had to deal with Fleetwood being a lot more direct. They didn’t carve open many opportunities from open play and when we gave away free-kicks, we dealt with them well. The defensive display was brilliant.
'I would like us to be a bit better at putting the game to bed and that was the only disappointment for me.'
Mousinho praised his players for adapting to a new three-at-the-back formation forced by an injury in the week to Joe Rafferty that left them without a recognised right-back: 'We didn’t have a right-back because Joe had picked up a slight neck injury earlier in the week. We thought it would loosen up, but he wasn’t able to travel up with us and it’s something we’ve been working on a little bit in training.
'Players should be flexible enough to fit into different systems and it was just guys playing out of position, like Terry Devlin, but he’s such an honest kid and performed magnificently.'