On a night prefaced by the surprise omission of the veteran goalkeeper Neville Southall from the Everton line-up, Scunthorpe could count themselves unlucky not to have dealt another reverse to a side eliminated by Portsmouth, Millwall and York at this stage of the competition in the last three seasons.
Paul Gerrard, called up as a clearly nervous replacement for Southall, had a torrid evening, fumbling more than once in a first-half dominated by the home side. He suffered a horrible moment early in the second period when the ball squirted through his hands after a wind-assisted cross deceived him, fortunately spinning away for a corner.
The young goalkeeper redeemed himself with some fine saves, however, not least when he somehow managed to prevent a fierce close-range shot by the striker Jamie Forrester gaining Scunthorpe what would have been a well-deserved equaliser.
Everton, third from bottom of the Premiership, looked unsure of themselves throughout, reflecting the air of uncertainty currently surrounding the club, where the future of the England forward Nick Barmby seems increasingly bleak following his failure even to make the squad for last night's match.
Under pressure throughout from a side exhibiting skill as well as passion, they were relieved indeed when Farrelly put them ahead after 36 minutes, the 21-year-old midfielder taking his chance clinically after Danny Williamson's through pass had caught out the Scunthorpe defence as they pushed up in search of an offside flag.
It was to Scunthorpe's credit that they bounced back strongly from a goal against the run of play and David D'Auria was close to putting them level early in the second period, when Gerrard conjured another daring stop.
His counterpart, Tim Clarke, then denied Everton the cushion of a second goal by keeping out shots from Farrelly, Gary Speed and Duncan Ferguson.
Scunthorpe United (5-3-2): Clarke; Housham, Sertori, Laws, Hope, McAuley; D'Auria, Walker, Calvo-Garcia; Forrester, Eyre. Substitutes not used: Harsley, Neil, Shakespeare.
Everton (3-5-2): Gerrard; Short, Watson, Bilic; Stuart, Williamson, Farrelly, Speed, Hinchcliffe; Oster (Cadamarteri, 76), Ferguson. Substitutes not used: McCann, Southall (gk).
Referee: M Reed (Birmingham).