Michael Smith was on target as Pompey saw off Carlisle to make it back-to-back victories.
Following a slow first half, the Blues were much better after the break and created a number of opportunities.
They were only able to take one – with Smith sliding home from a tight angle – but that proved enough to claim all three points.
Paul Cook stuck with the same side that comprehensively beat Notts County on Good Friday.
And they got off to an encouraging start as Gary Roberts met Adam McGurk’s cross, only to see his goal-bound header blocked before it could reach its intended target.
Kyle Bennett then sent in a decent delivery following good work down the left, but it was headed clear and Danny Hollands’ volleyed the loose ball over.
And Ben Davies was not too far away when he attempted a free-kick from 35 yards, curling the ball narrowly past the post.
Carlisle’s first proper chance arrived on 14 minutes and Mark Ellis should have at least hit the target when he was found in space inside the box.
There were not an abundance of chances to get the crowd of their feet, although the hosts were trying their best to up the tempo with some pressing high up the pitch.
United keeper Mark Gillespie did well to claim the ball just underneath his crossbar after Enda Stevens’ cross took a wicked deflection off Tom Miller.
Jason Kennedy had a couple of chances at the other end of the pitch, but dragged one effort wide before failing to find the target from a tight angle.
And, just before the break, Stevens received the first booking of the game following a crude lunge on Brandon Comley.
Carlisle United 0
The Blues came quickly out of the traps, but Gillespie claimed Christian Burgess’ dangerous cross and then saved Bennett’s shot at his near post.
And it was another effort from Bennett that led to the hosts breaking the deadlock on 57 minutes.
After some patient passing build-up, the winger’s curler from the edge of the box was spilled by Gillespie and SMITH forced the ball home from an acute angle.
Pompey might have added another moments later, but Roberts could not get enough power on his shot and it was comfortably saved.
There was still an attritional element to proceedings, however, with plenty of fouls to break up the flow of the game.
Carlisle threw on a couple of extra strikers in Derek Asamoah and Jabo Ibehre to try to find a leveller.
But the Blues were inches away from doubling their advantage following a quick counter-attack on 79 minutes.
Paul Jones punched a corner clear and Pompey broke up the pitch, with Michael Doyle and Roberts combining to tee-up McGurk, who burst through on goal and fired against the base of the post.
And both sides then had excellent chances to add to the scoring in a hectic couple of minutes.
First, Smith was denied by a fine save by Gillespie, with Danny Grainger getting across quickly to stop McGurk converting the loose ball.
United immediately went up the other end of the pitch, where Hallam Hope somehow failed to connect with Derek Asamoah’s cross at the far post.
It was Pompey who looked the more likely to score in the closing stages, but Jabo Ibehre wasted a great chance to level at the death when he hooked over from inside the box.
Pompey (4-2-3-1): Jones; Davies, Burgess, Clarke, Stevens; Hollands, Doyle (c); McGurk (McNulty 89), Roberts (Naismith 86), Bennett (Evans 90+3); Smith
Goals: Smith 57
Subs not used: Fulton, Webster, Close, Chaplin
Carlisle (4-2-3-1): Gillespie; Miller, Raynes, Ellis (Ibehre 77), Grainger (c); Comley (Asamoah 68), Joyce; Stacey (Gilliead 59), Kennedy, Hope; Wyke
Subs not used: Hanford, Atkinson, Gillesphey, Sweeney
Referee: Charles Breakspear
Attendance: 15,416 (361 away fans)