It appeared it would be one of those nights at the JJB Stadium as the Latics' mostly second-string outfit - Jewell having made nine changes - conjured chance after chance without reward.
• Souness raging as Latics progress
But, with extra-time looming, referee Steve Bennett correctly pointed to the spot when Jason Roberts was held in the area by Robbie Elliott, allowing Connolly to beat Republic of Ireland team-mate Shay Given.
It was just reward for Wigan, despite all the changes, with goalkeeper Mike Pollitt and left-winger Lee McCulloch the only survivors from Saturday's 2-1 home defeat to Spurs.
Yet this was no junior line-up as the majority of the side comprised those players at the heart of Wigan's promotion from the Coca-Cola Championship in May in Steve McMillan, Matt Jackson, Emerson Thome, Andreas Johansson, Gary Teale, Alan Mahon and McCulloch
Against a strong Newcastle line-up, with three changes made to the side beaten 1-0 at Everton on Sunday, they looked far from out of place.
They were joined in the side by Connolly, Australia midfielder Josip Skoko and England under-21 full-back Ryan Taylor, who was a thorn in the side of Souness' team all evening.
The Scot has surely not witnessed such a one-sided affair for some time as Wigan totally dominated the opening 45 minutes, and the majority of the second, with their superiority underlined in the first half by a corner count of 11-0.
Yet, via a combination of superb goalkeeping from Given - although he was lucky to get away with dropping the ball at two of those corners - and woeful finishing, the Magpies somehow headed into the break on level terms.
Jewell's side should have opened the scoring inside 60 seconds, with Connolly delivering a low ball into the near post where a fast-arriving McCulloch sidefooted wide.
That was the story of the first half, though, as chances went begging at regular intervals, with McCulloch then denied in the 15th minute by a full-stretch, fingertip save from Given.
Following that, Johansson twice spurned opportunities, with the second of those more clear cut as he failed to connect cleanly with a delightful Taylor cross from the right, albeit while under pressure from Peter Ramage.
After Thome received an accidental whack in the face on the half hour from Scott Parker, with the experienced Stephane Henchoz his replacement, Wigan then proceeded to get closer and closer.
In the 34th minute, McCulloch came within inches of breaking the deadlock as an angled drive shaved the crossbar before Nolberto Solano cleared a Matt Jackson header off the line soon after.
Then came a moment that summed up Wigan's half as Given first blocked a low McCulloch drive, yet with the goal gaping as he followed in for the rebound, Connolly scuffed the loose ball into the grateful arms of his Republic comrade.
When the interval came it was a blessed relief for Newcastle, affording them a breather and chance to regroup.
The break undoubtedly knocked Wigan out of their stride as they struggled to regain the earlier firm footing they had so clearly enjoyed.
Newcastle's first chance materialised in the 48th minute, with Parker inches wide of the right-hand post with a first-time drive from the edge of the area.
A number of corners followed before Emre then came closest of all midway in the second half by cracking the base of the left -hand post with a raking 25-yard drive.
Yet Wigan soon regained the upper hand, only for more shake-of-the-head moments.
Henchoz initially picked out a marauding Teale down the right wing who in turn played in Connolly for a miscue from eight yards, yet into the path of Mahon who proceeded to hit the sidenetting when it appeared easier to score.
Yet Wigan's luck appeared to be right out as Given then brilliantly saved from Roberts, who had earlier replaced Johansson, before Faye blocked McCulloch's searing drive from point-blank range on the rebound.
But, with the extra 30 minutes on the cards, Bennett intervened and Connolly made no mistake to further add to Souness' woes.
Souness raging as Latics progressNewcastle manager Graham Souness was left fuming with his side following their shameful exit from the Carling Cup.The Magpies were thoroughly outplayed by a 'second-string' Wigan team at the JJB Stadium, although the Latics required a late penalty to clinch their place in the last eight.
As Wigan boss Paul Jewell pointed out, though, it was 'a 1-0 hammering' as the home side dominated the fourth-round tie virtually from start to finish.
In particular, Newcastle failed to show up in the opening half as a Wigan team showing nine changes from the one beaten 2-1 at home to Tottenham on Saturday created chance after chance, with a corner count of 11-0 underlining their superiority.
But a combination of fine goalkeeping from Shay Given and poor finishing contributed to the goal-less half-time scoreline, allowing Souness to regroup at the interval.
The visitors briefly sparked into life at the start of the second period, with Scott Parker narrowly wide and Emre striking the base of the left-hand post, but Wigan soon regained the initiative.
Opportunities continued to be spurned, however, and extra-time appeared to be looming until Robbie Elliott was adjudged to have held substitute Jason Roberts in the area, allowing David Connolly to steer home the spot-kick in the 88th minute.
'I am most definitely angry,' seethed Souness, who had the near 5,000 Newcastle fans turn on him after the final whistle.
'We have let down every single person who has travelled from Tyneside, and I can understand their reaction.
'I cannot complain at that. I am a big boy and I know if I was a supporter who had spent whatever they had done to watch this game then I would be unhappy at watching a team play the way they did, especially in the first 45 minutes.
'It's been a long time since one of my teams was outplayed like that. We were poor and the game should have been over by half-time.
'They were totally dominant, and although the penalty was a wee bit unfair, we are not complaining about it too much because the best team won.'
Souness refused to offer complacency as an excuse, adding: 'You cannot think it is going to be an easy game because you are playing against some players you have not heard of before.
'To the foreign lads we pointed out to them that cup football in this country is not like it is on the Continent where it is not taken as seriously.
'We told them it would be a hard game. We went over that before they went out there, but they didn't heed the warning.
'The one thing a player should be able to guarantee is that he gives 100% when he crosses the white line but not every one of my players did that tonight.'
For Jewell, the ultimate goal remains Premiership survival as he said: 'We still have to be realistic as our aim is to stay in this league.
'If you offered me the choice now of winning our next three league games against Liverpool, Chelsea and Manchester United or winning the Carling Cup, then I would take winning the three Premiership matches.
'Don't get me wrong, I would love to do both, but we want to stay up at all costs, whatever it takes.'
Jewell, though, felt his side would never score despite their dominance, adding: 'I didn't think the goal was going to come.
'We played exceptionally well, and I thought the lads who came in were terrific.
'The penalty was a bit debatable but it was well deserved because we were the better team from start to finish.'
Wigan Athletic 1 - 0 Newcastle United
