There was a nervy period right at the second half of a damp contest at the Stadium of Light.
Pompey had led 2-1 at the break, with John Marquis restoring their advantage after Charlie Wyke cancelled out Marcus Harness’ opener.
The hosts, unsurprisingly, looked to hit back and apply some pressure, initially causing a few problems.
But the Blues’ overcame that and ultimately saw the game out with ease, making sure of the points through a late Marquis penalty.
Joe Gallen was delighted with the way they dealt with the Black Cats to climb up to fifth in the League One standings.
Pompey’s assistant manager said: “You have to expect Sunderland to come at you when you’re 2-1 ahead against them at half-time – and they did.
“They had a good chance within the opening seconds and we knew there would be a big period for us to overcome.
"There were three for us on this occasion – and there could have been more. I have to congratulate the players for that performance."
“But we also wanted to spring some surprises of our own and we were able to get another foothold, play some football in the middle third and break with real pace.
“The result gives the players so much confidence and belief in themselves because Sunderland had only conceded one league goal before facing us.
“There were three for us on this occasion – and there could have been more. I have to congratulate the players for that performance.
“We’ve done better away from home so far this season, but there are two games at Fratton Park coming up now and we need to put on a performance at Fratton Park.”
The one blow for Pompey was the sight of Michael Jacobs limping from the pitch early in the second half.
Gallen said: “I initially thought he’d hurt his ankle, but I think there’s an issue with his knee and there will be a scan to find out the extent of that.
“Unfortunately for us, I’m not too sure Michael’s going to be with us for the next few games. We have to see what the damage is.”