Leicester will be hoping to finally get lucky against Chelsea in the FA Cup quarter-finals after Ricardo Pereira’s late goal enabled them to overcome a hard-working Birmingham in the fifth round.

This is the third time since 2012 Leicester have made it to the last eight and been drawn against Chelsea. Now they will aim to go one stage further against their top-four rivals. “We’re happy to be at home – we’re happy to be in the competition still,” Brendan Rodgers said. “Chelsea had a great result [against Liverpool], a great performance, and we’ll relish the game.”

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The FA Cup can so often be seen by bigger clubs as a distraction but for Leicester, after winning only three of their past 12 Premier League games to limp into the new year, this run could hardly have come at a better time. “It was important to get back to our game tonight,” Rodgers added.

“Every team has a blip at some point in a season. But these players have been absolutely incredible through the course of this season and since I’ve been here – and their honesty will get them back to their level. Tonight, especially in the second half, that was much more like it.”

Qualifying for the Champions League with a top-four finish remains a realistic priority. But this hard-earned victory offers Leicester a fillip as they seek to regain their mojo. With Jamie Vardy expected back from a calf injury in time for Monday’s home game with Aston Villa, the season’s run-in suddenly looms more brightly.

Leicester dominated this Midlands match-up against an organised Birmingham side, who had not lost since New Year’s Day, but without making too many clear chances. Then just as extra time started to beckon, Ben Chilwell crossed from the left towards Kelechi Iheanacho at the far post. The ball fell out to Marc Albrighton who, at the second attempt, manipulated enough space to clip in a cross that saw Pereira – what was the right-back doing up there? – leap to head in his fifth goal of the season.

Rodgers was not surprised to see his right-back soaring into the six-yard box. “We were pushing, trying to get numbers in there,” he said. “He’s obviously going into the box to score. First of all he’s swapped positions with Marc, Marc’s gone to the right-back position and ended up crossing from out there. We have a structure to our team but it’s to attack, to score goals. We had to be patient but we got there.”

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It was Birmingham’s first defeat in 14 games and their supporters left proud of their team’s efforts. They even had the good grace to offer their former teenage prodigy, Demarai Gray, a departing chant – “He’s one of our own” – after the winger, starting for the first time against his first club, was substituted.

Birmingham omitted their latest youth sensation. Jude Bellingham has been the name of the Championship player on everyone’s lips this season and, amid speculation of intensified interest from Borussia Dortmund, the 16-year-old was again rested by Pep Clotet.

A St Andrew’s source said there had been no contact from the German club, while Clotet said Bellingham’s exclusion was nothing to do with the speculation.

“I’m not aware because I’m a head coach and recruitment – ins and outs – are not my business,” the manager said. “I have been focused on the game but let me cut [out] some speculation that might happen. First of all it is very good for a club like Birmingham to be able to attract the interest of so many big clubs for a player that makes it through the academy and who we play in the first team.

“But Jude was not here not for that reason. I wanted to give him a good rest and get him fresh for Saturday and Reading. He’s played a lot of games.”