Merson, who will cost Middlesbrough pounds 5m if they achieve promotion at the first attempt, fired Bryan Robson's side in front after just six minutes. But on the hour, Connelly, a free-transfer recruit from non-League football, equalised with only the second goal of a Stockport career spanning 200 games.
By curious coincidence, Connelly's previous strike came when Stockport won at the Riverside Stadium in the second leg of the Coca-Cola Cup semi- final last February, only for Boro to go through on aggregate.
That month, Merson appeared in England's World Cup defeat by Italy at Wembley. As a seemingly integral part of Arsenal's plans, he can hardly have envisaged that come September he would be stepping out at Stockport, who were then strictly Second Division. Yet he wasted no time in dispelling any doubts that he might be less than stimulated by the surroundings.
With the home defence caught square near the halfway line, Mikkel Beck slipped a Boro clearance over his head for Merson to sprint clear. A low drive to Eric Nixon's right from 18 yards brought his first goal for the Teessiders.
Stockport, without a win at the higher level, responded resiliently. Tony Dinning, who had earlier prevented Boro doubling their advantage with a textbook sliding tackle on Beck, had a goal-bound header blocked, as was Brett Angell's follow-up.
Despite the introduction of Andy Townsend, Boro were gradually hustled out of their stride.
That Stockport's point-saver should have come from a header was unsurprising. The shock was that it was Connelly, a 5ft 9ins wing-back, who materialised to glance the ball beyond Ben Roberts after Andy Mutch had headed a left- wing cross back into the danger area.
Stockport County (3-5-2): Nixon; Dinning, Woodthorpe, McIntosh; Connelly, Richardson (Mutch, 55), Marsden, Bennett, Searle; Armstrong, Angell. Substitutes not used: Cooper, Durkan.
Middlesborough (4-4-2): Roberts; Fleming, Vickers, Festa, Kinder; Stamp, Emerson, Mustoe, Moore (Townsend, 24); Merson, Beck. Substitutes not used: Liddle, Freestone.
Referee: S Baines (Chesterfield).