The result at a sunny Fratton Park also ended the visitors’ slim hopes of avoiding relegation to League Two.
It was midway through the first half when the key moment arrived, as Curtis completed a fine move with a neat finish.
Danny Cowley made a single change from the side that were beaten on the road at Swindon earlier in the week.
Charlie Daniels dropped to the bench to make way for George Byers, as Pompey switched to a 3-4-3 system.
Callum Johnson joined Sean Raggett and Rasmus Nicolaisen in the back-line, with Ryan Williams and Marcus Harness out wide.
Byers and Curtis were positioned either side of leading marksman John Marquis, who was making his 100th appearance for the club.
The game began at a frenetic pace, with both sides flying into challenges and looking to get forward when possible.
But there were few clear-cut chances to speak of and it took a while for the hosts to gain control of proceedings.
They soon began passing the ball around neatly on a carpet of a pitch, with Byers and Ben Close looking particularly pleasing in possession.
It was the visitors who were first to properly threaten, though, as Alex Rodman got past Nicolaisen and tried an angled shot that Craig MacGillivray got his fingertips to.
But Pompey broke the deadlock moments later, with a nice move that started with the keeper rolling the ball out to Close.
He then found CURTIS, who received a delightful return pass from Byers before expertly bending a shot into the bottom corner.
Nicolaisen came close to doubling the lead, rising highest to meet a Close free-kick and sending a header narrowly past the post.
Pompey were looking pretty much in control, but Rovers had a chance to level just before the interval.
A free-kick was not properly dealt and Rodman nodded the ball towards the line, with Raggett able to scramble it clear.
Bristol Rovers 0
The visitors looked to attack right from kick-off and a fierce long-range strike from Luke McCormick was gathered at the second attempt by MacGillivray.
A nice pass from Tom Naylor then found Williams on the left and Anssi Jaakkola did well to claim the Australian’s cross, with Marquis ready to pounce.
Rovers – who had nothing really to lose – were certainly posing more of a threat as the second half progressed.
But the back three were holding their own and denying the opposition forward line a clear sight of MacGillivray’s goal.
Cowley made a change just past the hour mark, with Andy Cannon – who has been nursing a back problem – replacing Close.
Pompey began to take control again, with Byers, Harness and Marquis all seeing efforts blocked in quick succession.
Another change saw the impressive Byers make way for Harvey White, with Cowley looking for some fresh energy.
Daniels and James Bolton then came on for Williams and Harness to shore up the wing-back positions.
A superb long pass from White picked out Curtis in space on 80 minutes, but the Republic of Ireland international could not find the target with a curling shot.
And Pompey saw out the closing stages with relative ease to claim the three points that boosts their hopes of a top six finish.
Pompey (3-4-3): MacGillivray; Johnson, Raggett, Nicolaisen; Harness (Bolton 77), Close (Cannon 63), Naylor (c), Williams (Daniels 77); Byers (White 70), Marquis, Curtis
Goals: Curtis 27
Subs not used: Ward, Downing, Stanley
Bristol Rovers (4-4-2): Jaakkola; Williams, Kilgour (Hare 84), Baldwin, Leahy (c); Rodman (Hargreaves 75), Martinez (Little 84), McCormick, Westbrooke (Oztumer 59); Hanlan, Daly (Walker 75)
Subs not used: Day, Tutonda
Referee: Thomas Bramall