Goals from Shaun Whalley – just five minutes after he had a penalty saved by Luke McGee – and substitute Stefan Payne wrapped up another good day’s work for Hurst’s side.
Shrewsbury’s latest victory sets them up nicely for their Boxing Day trip to leaders Wigan Athletic.
Hurst, pleased with how his side performed against Pompey, said: “I thought it was very good because we have to take into account the opposition and against a team I think are second in the form table over a length of time and been in very good form.
“I thought overall we dominated for large parts, might not have still created tonnes of chances, but I still think that we looked the best side realistically and what we’re doing, certainly at home, is making teams defend, and putting them on the back foot for large parts.”
Hurst was impressed how Whalley and his team-mates responded to the disappointment of the winger’s 54th-minute spot-kick being saved by McGee as he quickly made amends by scoring the opening goal.
“You’ve got to keep your head,” he said. “I thought he had just a very small period where it looked like he’d lost himself.
“He’ll be upset that he’s missed a chance to score another penalty, but a great follow up and response, from not only him but the team because it can really affect you when you think it’s going to be a tight game and perhaps your opportunity might have gone.
“But we kept going and I thought we were worthy of maybe winning slightly more comfortably than we have done on many occasions this season.”
Portsmouth found chances hard to come by although home goalkeeper Dean Henderson did well to stop a Brett Pitman free-kick shortly before making the breakthrough.
Pompey manager Kenny Jackett said: “We didn’t do enough going forward – I thought right the way through the game – to be able to pull around or get in behind a very-well organised Shrewsbury side.
“They’ve only conceded 14 goals which after Wigan (12) is the best in the league. That’s why they’re second in the table, but the intensity of their closing down, you could see from the second goal is there.
“They have good enthusiasm and for us to be able to get away and be able to create chances, we needed to work harder at that than we did today.”
Jackett is now seeking a positive response from his side when they host AFC Wimbledon on Boxing Day.
He said: “It’s good when you lose that you have a game within two days, that’s a good thing, and it’s a home game as well.
“We’ll learn from this. We didn’t do enough I didn’t think going forward to really get any points, that’s the main reason.”
Paul Huntington says Preston's play-off hopes this season hinge on them getting the balance right on and off the pitch.