Sheffield United are gathering momentum that could change them beyond recognition but the wonder of their rise is that so many of those instrumental to it have known days when none of this seemed remotely possible.

Billy Sharp rejoined them for a third spell five years ago and his metronomic ability to plunder goals seemed in vain given United immediately finished 11th in the third tier. So there is plenty to celebrate in the fact that, in the winter of his career and with the picture so different, he remains capable of popping up with contributions that could matter profoundly.

His latest arrived midway through extra time in an FA Cup tie in which United had been well short of their best. Reading had pushed them hard, an eventuality that seemed remote when David McGoldrick scored after 85 seconds, but they found the moment of quality sides from a higher level are obliged to muster.

Luke Freeman had been one of their better performers and when he darted to the left byline there was always the chance a poacher of Sharp’s quality would sniff a yard of space if the delivery was right. In the event it gave the 34-year-old, who had arrived as a late substitute in normal time, an open invitation to finish and afforded Chris Wilder the platform to eulogise about his club captain.

“He’s still got life in him and I’m sure he’ll tell you that as well,” he said. “Who’s to say he’s not got a little bit more left in the tank? He’s just a natural finisher, it was a brilliant goal for us and a fantastic finish.”

It was Sharp’s third goal of the campaign on a night that had already turned up a good-news story involving a Blades striker. McGoldrick has played exceptionally this season, even if injuries have hampered him since January, but did not have a goal to show for his endeavours in his past 23 club games. He put that right with a well-timed downwards header from Ben Osborn’s cross before the game had settled and, at that stage, a regulation win seemed likely.

But Reading, ensconced in mid-table Championship drudgery, made a fist of what Mark Bowen had described as their biggest game of the season. They stabilised and equalised two minutes before half-time when George Puscas converted a penalty after George Baldock was adjudged to have pushed Andy Rinomhota.

Bowen could reflect on a positive night’s work given Reading were the better side for much of the second half and refused to be deflated later on by Sharp’s goal, twice coming close to forcing penalties. “After a terrible start we played our own stuff and for large periods took the game to them,” he said. “It’s hard to take tonight.”

In the end, though, Wilder could reflect that his team found a way to win. The door to European football is wide open now and it says everything about their top-flight season that, two games from the final, the FA Cup is not even their most likely route. “I honestly don’t know where we can take this season,” he said. “They just roll on to the next challenge.”