They were in charge for most of the contest, but had to wait until the closing stages of the first half before Marcus Harness increased his goal tally.
And they were rewarded for their overall play after the break, with George Hirst doubling the lead and Reeco Hackett wrapping things up at the death.
Danny Cowley made three changes from the side that dramatically beat AFC Wimbledon on home soil at the weekend.
Kieron Freeman came in for the suspended Lee Brown, but started in the centre of defence, with the Blues switching to a 3-4-1-2 system.
There were also starts for Hackett – as a left-sided wing-back – and Joe Morrell, as Michael Jacobs and Louis Thompson dropped to the bench.
With the absence of Clark Robertson and Brown, former Imps hero Sean Raggett was handed the captain’s armband.
Pompey dominated the first half and created a number of promising openings, but were often let down by the final ball.
An early Shaun Williams corner was turned wide by Raggett, while a deflected Ronan Curtis effort was diverted behind by Josh Griffiths.
And the Imps keeper was called into action again from the resulting corner, which was fired towards goal by Connor Ogilvie.
Curtis miscued another shot narrowly past the post and Ogilvie then saw his goal-bound drive cleared from the line by Lewis Montsma.
The momentum faded after that, although the Blues were still looking the stronger team, with Williams and Morrell – the latter facing his former club – dominating in midfield.
They received a blow when Raggett was – rather harshly – booked for a foul in the middle of the pitch on 28 minutes.
It was the defender’s fifth yellow card of the season and, just before an amnesty kicks in, means he will be suspended for Saturday’s trip to Gillingham.
There had not been too much trouble at the other end, although the home support wanted a penalty when Hackett eased Lasse Sorensen off the ball inside the area.
The breakthrough almost came in stoppage-time, as Hirst charged his way up the pitch and past a couple of challenges before forcing a save from Griffiths.
But there was still time for Pompey to take the lead before the break – and there was no surprise to see who scored.
Mahlon Romeo found Hirst in the box and although he was denied, the loose ball ran for HARNESS to fire home in a fourth successive appearance.
Lincoln CIty 0
An early opportunity for Harness was stabbed wide, as the Blues looked to build on their lead once the action restarted.
And they went a lot closer to finding a second goal following some good work from Curtis along the edge of the box.
He eventually picked out Romeo on the right and the wing-back’s low effort struck the inside of the post and bounced back out.
But the Imps began to pick up the pace and former Fratton loanee Chris Maguire curled a shot narrowly over after cutting inside from the left.
Just as they were starting to get into the ascendency, however, the visitors doubled their lead – much to the delight of the noisy travelling army.
Harness slipped a neat pass through to Curtis, who unselfishly squared the ball for HIRST to slide home his first league goal for the club.
Lincoln tried to find a path back into the contest, but Gavin Bazunu did well to deny Hakeeb Adelakun from point-blank range.
Cowley then freshened things up with a couple of changes in quick succession, as Jacobs came on for Hirst before Thompson replaced Morrell.
And a third substitution followed on 80 minutes, with Harness making way for the fit-again Ellis Harrison.
Pompey appeared to be coasting towards the final whistle, but there was further reason to celebrate towards the end.
Harrison was brought down on the edge of the box and although the free-kick from HACKETT hit the wall, he was first to the loose ball to slam it into the net.
Lincoln (4-1-4-1): Griffiths; Poole, Montsma, Eyoma, Robson; McGrandles (c); Bishop (Nlundulu 58), Sorensen (Adelakun 68), Maguire, Fiorini; Draper (Sanders 86)
Booked: Montsma, Maguire
Subs not used: Long, Jackson, Roughan, Gallagher
Pompey (3-4-1-2): Bazunu; Freeman, Raggett (c), Ogilvie; Romeo, Morrell (Thompson 76), Williams, Hackett; Harness (Harrison 80); Curtis, Hirst (Jacobs 73)
Goals: Harness 45+3, Hirst 66, Hackett 89
Booked: Raggett, Morrell
Subs not used: Bass, Vincent, Azeez, Gassan
Referee: Ross Joyce
Attendance: 8,533 (746 Pompey fans)