Fighting against odds of 80-1, Jones' Second Division battlers took five minutes to slice in half the 2-0 deficit they carried with them from the first leg. Connelly, Stockport's right-back and assistant physiotherapist, struck the early blow that gave the underdogs a fighting chance of meeting Leicester at Wembley on 6 April.
By the final whistle, though, they were still a goal short - and a player too, Tony Dinning having been sent off for his part in an off-the-ball tussle with Fabrizio Ravanelli with quarter of an hour left.
The Middlesbrough players paraded on their lap of honour in the special edition shirts they will wear at Wembley. The job lot jerseys might have been surplus to requirements, however, had Mark Schwarzer's outstretched left leg not kept out what seemed a certain goal when Gianluca Festa gifted a clear chance to Louis Cavaco 20 minutes from time.
For that, Bryan Robson had Terry Venables to thank, Australia's football director having granted the Sydney-born goalkeeper permission to skip last night's 1-0 victory over Macedonia. "I'm just relieved that we're through," Robson said as the Middlesbrough fans enjoyed the prospect of the club's first appearance in a major cup final in their 121-year history.
Wembley is not quite uncharted territory for Boro, although the 1-0 defeat they suffered beneath the twin towers against Chelsea seven years ago was in the final of the Zenith Data Systems Cup. The two-goal cushion they built at Edgeley Park was sufficient for the commercial department at the Riverside to put their shirts on Robson's players making it to a first-class final. And their faith seemed justified as the genial Juninho threatened to spirit away Stockport's challenge in the opening three minutes.
First the boy from Brazil ghosted through the Stockport defence and teed up Mikkel Beck for a shot the Dane clipped off the outer angle of bar and post. Then Juninho applied the finish to his own opening, driving inches wide from the right edge of the box.
At that stage, the 3,000 Stockport fans must have been questioning the point of their trek to Teesside. By the sixth minute, however, several of them were on the pitch celebrating. Mike Flynn, Stockport's captain and at pounds 150,000 their most expensive acquisition, hoisted a free-kick and Connelly prised through the home defence, playing a wall-pass with Alun Armstrong, before beating Schwarzer with a fiercely struck drive.
The Middlesbrough goalkeeper was exposed again a minute later and his colleagues were deeply in his debt when he managed to block Chris Marsden's angled shot.
The mood among the natives shifted from one of premature celebration to concerned restlessness and it was not until the 43rd minute that Middlesbrough troubled the visitors again, Paul Jones pushing a looping Beck header on to and over his bar.
The man of the match sponsor - listed on the team-sheet as "anonymous" - could well have been Fabrizio Ravanelli, for all the influence the Italian exerted on the first half. Within two minutes of the break, though, he drifted wide on the right and delivered a cross Beck headed narrowly wide of the target.
Having survived that scare, Stockport responded with a charging run from midfield by Marsden, who got past all of the red-shirted players in his path but was thwarted by Schwarzer, who burst from his line and braved a two-footed challenge to grasp the ball.
If Marsden was fortunate to escape with a yellow card, he and his colleagues were counting their blessings just before the hour. With only Paul Jones to beat, Juninho had the home crowd groaning as he lofted the ball on to the bar.
There were groans, too, amid the post-match celebrations. West Ham United's victory at Chelsea may yet prove the most significant result for Middlesbrough last night.
As Robson remarked: "It's important that we beat Leicester." He was talking about his side's "cup final" at Filbert Street on Saturday.
Middlesbrough (4-3-1-2): Schwarzer; Cox, Pearson, Festa, Fleming; Mustoe (Blackmore, 21), Emerson, Hignett; Juninho; Ravanelli, Beck. Substitutes not used: Vickers, Roberts (gk).
Stockport County (4-4-2): Jones; Connelly, Flynn, Bennett, Todd; Jeffers (Nash, 87), Dinning, Cavaco (Gannon, 75), Marsden; Mutch (Angell, 75), Armstrong.
Referee: P Jones (Loughborough).Reuse content