Jack Baldwin headed Pools in front after 18 minutes, before James Poole doubled their advantage seven minutes after the break.
Pompey youngster Jed Wallace pulled one back for the home side after 67 minutes, but Hartlepool substitute Greg Rutherford netted a third in stoppage time to seal their third victory of the season.
Hughes' men are now 10 points from safety and the Pools boss hopes his side can show the composure needed to close out more games.
He said: "I just hope the games don't run out. But you have to look for inspiration and inspiration can come from so many different places.
"A few weeks ago we went to Sheffield United, and turned them over on their own patch. That gives me inspiration. That tells me as a manager that we're capable of beating most teams in this league.
"But I'm also aware that trepidation can creep into your game, especially when you're winning a match.
"You can feel you have something to lose, but we just have to overcome that. It's time they rolled their sleeves up and when it comes to expectation, we just need to deal with it.
"You have to be a man, go on that stage, deal with the pressure and produce a performance. We have to do that as a team.
"We've got 18 games and 18 cup finals to go. That was the first of them. It's all about digging in and getting results."