So much of Chelsea’s campaign has been tempestuous, a season played out to the grumbling of a disenchanted head coach, but it could yet produce a trophy. It took a header in extra time, scored by one of the smallest players on the pitch, to see off Leicester City, and as those in the away end chorused their delight at another imminent trip to Wembley, Antonio Conte could still cling to the possibility of a send-off at the national stadium. If he is to depart this club in May, there might be no better way to go.

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The Premier League champions needed this. That midweek exit in the Champions League, while hardly surprising given Barcelona’s reputation, had still stung, and the prospect of leaving the East Midlands with nothing more than the pursuit of a top-four finish to sustain interest over the next two months would have been unpalatable. Now they will meet the relegation-threatened Southampton in next month’s semi-final, with the possibility of last season’s FA Cup finalists going one better this time maintained.

There was something rather apt about the unlikely nature of Chelsea’s winner. This had been a frantic mess of a cup tie, exhilarating and infuriating in equal measures. Goals had been exchanged in normal time to prompt the anxiety of the extra half-hour, in which Pedro would provide the decisive contribution.

The substitute actually sparked the break which would lead to his winner, collecting inside his own half before shifting possession upfield to Álvaro Morata and ambling forward unnoticed. Morata had supplied N’Golo Kanté, with the former Leicester midfielder using Marcos Alonso’s dart down the touchline as a decoy to draw Wes Morgan from the middle.

Play Video 0:42 Antonio Conte pleased with Chelsea's character after FA Cup win at Leicester – video

Kanté was still offered far too much time to measure his centre and pick out Pedro, eagerly infiltrating space between Ben Chilwell and Marc Albrighton, an unsatisfactory last line of defence with the home side’s centre-halves horribly out of position. The winger, at 5ft 7in, duly leapt to connect before Kasper Schmeichel could punch, and nodded his team’s second neatly over the muddle and Chelsea into the semi-finals. “Maybe he has only ever scored twice with a header: today and our third here last season,” said Conte of the winger’s impact. “It’s great for him, and great for the team. Pedro is another player who puts, in every moment, everything he has for the team. If he starts the game or if he comes on. I’m very happy for him.”

It was a winner to deflate the mood inside this arena, all the optimism built up by Jamie Vardy’s equaliser back in normal time suddenly punctured. Harry Maguire would fizz the ball across Willy Caballero’s six-yard box in what time remained, prompting panic yet no reward, but that was as close as Leicester would come to forcing parity for a second time. The locals watched the draw being made post-match and will have cursed a missed opportunity.

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“Of course we are frustrated,” mumbled Claude Puel, a former Southampton manager. “We deserved a fairer result. It’s harsh because my players gave their best, and demonstrated fantastic attitude and commitment. I can’t criticise the squad or the players. Now we have to keep this positive attitude and quality on the pitch to finish the season strongly.”

That will be in pursuit of a top-seven finish, even if Puel will still be wondering what might have been. The Frenchman would have been convinced momentum had been wrested back in the tie going into the extra period. Leicester, for all their initial urgency, might have trailed at the interval to Morata’s well-taken opener but forced themselves level 14 minutes from time as Chelsea’s concentration momentarily wavered. Riyad Mahrez was permitted to ease beyond Alonso far too easily on the flank, with his centre prodded at goal by Vardy only to strike Andreas Christensen inside the six-yard box. In the confusion which followed the ball broke to Vicente Iborra, whose first attempt struck the prone César Azpilicueta, and his follow-up was blocked splendidly by a diving Caballero.

Thereafter, the Argentinian’s luck deserted him. With the six-yard box littered with bodies, the ball spun away from the goalkeeper’s attempt to smother and was rammed home by Vardy. Even then the goalkeeper somehow laid a glove on the shot, but was in no position to keep it out. He would at least make amends with a smart save from the England striker as time ticked down.

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Conte waved his players off on international duty bolstered by Pedro’s contribution, but also by Morata’s return to some semblance of form. The striker had not scored since Boxing Day but despite a nervy start, has at last made his mark on the calendar year. A Leicester attack had run aground three minutes from the interval, momentum squandered by Kelechi Iheanacho’s slack pass to Mahrez, who eventually surrendered possession to Alonso. Willian, prodded clear by Antonio Rüdiger, would wrestle himself free of Chilwell’s attentions and prise Leicester apart, with his diagonal pass sending Morata galloping between and beyond Morgan and Danny Simpson.

The striker took a touch, opened up his body and curled his effort into the far corner. “It was very important for him to score, but at the same time I was very pleased with his whole performance,” added Conte. “He showed great character and that he is strong. This goal will be very important for the future.” As it was, Pedro’s may prove to have been just as critical in sustaining this team’s aspiration for a trophy.