The Whites were handed the chance to equalise in the FA Cup third round tie in Wales after Rodrigo halved the deficit in the 65th minute.
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Junior Firpo looked to have got the visitors back on level terms, only for Bagan to turn the ball away with his hand to stop it nestling into the corner.
Unsurprisingly, he didn't get away with it where he was quickly brandished a red card in the 80th minute.
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But it proved to be worth it, as just like what Suarez did for Uruguay in the 2010 World Cup quarter-final against Ghana, the subsequent spot-kick was missed.
Rodrigo failed to score his second of the match - and crucially the equaliser - after his effort from 12 yards was saved by Jak Alnwick.
It was redemption for Alnwick who should have done better when Rodrigo headed past him just after the hour mark.
Speaking on talkSPORT commentary, Stuart Pearce said: "Certainly it was worth taking the red card with the missed penalty."
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It looked to be as if Cardiff were to hold on for the victory to book their place in the fourth round at the expense of the Premier League side.
But the Championship strugglers succumbed to a late goal in the third minute of added time after 18-year-old Sonny Perkins bundled the ball home from close range.
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Cardiff hoped for the offside flag to be raised, but it wasn't given to spark wild celebrations from the Leeds players and fans.
Bagan's red card ultimately proved to be decisive as Leeds snatched a 2-2 draw to force a replay at Elland Road later this month.
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Cardiff went into the break 2-0 up thanks to goals from Aston Villa loanee Jaden Philogene and ex-Liverpool striker Sheyi Ojo.
Leeds barely threatened in the first half, but dominated the second period with Rodrigo's header from a corner getting the Yorkshire back into the game.
And Rodrigo can be thankful for Perkins sparing his blushes after firing home from two yards out at the death.
The draw ends Leeds' shocking run of losing their last six FA Cup matches.
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