Conor Shaughnessy grabbed a stoppage-time winner to ensure Pompey maintained their spot at the League One summit.
The centre-back repeated his Wycombe heroics from earlier in the month by converting a Jack Sparkes corner.
They had dominated much of the contest, but it looked as though the hosts would pay for their profligacy until Shaughnessy’s last-gasp intervention.
John Mousinho made three changes from the side that beat Port Vale in the last league game before the international break.
Regan Poole and Alex Robertson both returned from suspension, while there was also a start for Tino Anjorin, as Sean Raggett, Ben Stevenson and Christian Saydee all dropped to the bench.
A period of silence took place before kick-off to remember the innocent victims of the devastating events in Israel and Palestine.
Pompey dominated possession throughout the first half and created a number of chances to break the deadlock.
The first fell for Robertson, whose fierce effort towards the top corner was claimed by Tomáš Holý following good work from Abu Kamara and Anjorin.
Shaughnessy then slipped a fine pass through to Sparkes and although he could not get a shot away, the full-back eventually swung in a fine cross.
It was met by Colby Bishop in the box and a glancing header from the prolific striker was saved by Holý.
He soon met another dangerous delivery, this time from Anjorin, and nodded narrowly over the bar.
Carlisle had not threatened too much at the other end, but they had a decent opportunity when Jack Armer found Alfie McCalmont in the area.
The midfielder drilled the ball towards the target and it ricocheted off Shaughnessy and into the arms of Will Norris.
Pompey were still looking the more likely side to open the scoring and Paddy Lane scuffed a good chance straight at Holý after collecting Anjorin’s glorious pass.
Then, with the rain starting to fall, Bishop turned a Sparkes cross wide, as the home side continued to knock at the door.
And the striker could not get a shot away from a few yards out after a tackle on Lane saw the ball bounce into his path.
Half Time: Pompey 0 Carlisle 0
The Blues were caught napping straight from the restart and were left feeling relieved not to fall behind.
McCalmont received the ball in acres of space inside the box and rolled a low shot against the base of the post.
An Owen Moxon corner then caused more problems moments later, but skipper Sam Lavelle could only prod straight at Norris.
Mousinho looked to freshen things up with a change just before the hour mark, as Anjorin made way for Saydee.
The hosts were starting to find a bit more rhythm again and Holý got down low to his left to deal with a long-range Lane effort.
It was beginning to reflect the first half, with Pompey dominating possession and looking to apply pressure.
Holý got down to his right to deal with a 30-yard Sparkes free-kick after the lively Joe Morrell had been bundled to the turf.
Another substitution followed for the hosts on 77 minutes, with Lane being replaced by Australian striker Kusini Yengi.
But it was the Cumbrians who almost grabbed a late goal, with Norris making a superb save to turn Dan Butterworth’s shot around the post.
Instead it was the Blues who made the most of the stoppage-time drama after Holý had tipped Bishop’s header over the bar.
The corner was whipped into the box by Sparkes and SHAUGHNESSY got to the ball first to head it home and keep Pompey top of the table.
Pompey (4-2-3-1): Norris; Rafferty, Poole, Shaughnessy, Sparkes; Robertson (Raggett 90+5), Morrell (c); Lane (Yengi 77), Anjorin (Saydee 58), Kamara; Bishop
Goals: Shaughnessy 90+3
Booked: Rafferty
Subs not used: Schofield, Ogilvie, Stevenson, Devlin
Carlisle (4-1-4-1): Holý; Back, Lavelle (c), Mellish, Armer; Guy (Robinson 84); Maguire, McCalmont (Butterworth 69), Moxon, Gibson; Garner (Plange 78)
Booked: McCalmont, Guy, Garner
Subs not used: Breeze, Barclay, Ablade, Edmondson
Referee: Leigh Doughty
Attendance: 17,911 (676 away fans)