England Under-19 international Sonny Perkins kept Leeds in the FA Cup as with a dramatic stoppage-time equaliser earning them a 2-2 draw at Cardiff.
Cardiff looked like inflicting more FA Cup third-round misery on Leeds following first-half goals from Jaden Philogene and Sheyi Ojo.
But Rodrigo reduced the deficit with a close-range header and, after the Spanish substitute had been denied from the penalty spot and Cardiff lost Joel Bagan to a red card, Perkins squeezed home from close range three minutes into injury time.
The tie had evoked memories of Cardiff’s famous third-round victory in 2002 when David O’Leary’s Leeds were top of the Premier League.
Cardiff were in the third tier at the time, but a frenzied Ninian Park saw Scott Young’s late winner deliver one of the competition’s great upsets.
Former defender Young was among the guests invited back for the day as around 6,500 Leeds filled the end behind one of the goals at Cardiff City Stadium to produce a terrific atmosphere.
Both Cardiff manager Mark Hudson and Leeds counterpart Jesse Marsch rang the changes with their respective positions in the Championship and the Premier League of some concern.
Only three Cardiff players remained from their New Year’s Day defeat at Blackburn, while Leeds kept four from the 2-2 home draw with West Ham.
Leeds were playing their 10th consecutive FA Cup away tie – just one short of Stockport’s 11-game record in the competition – but started well with Crysencio Summerville and Wilfried Gnonto lively and Darko Gyabi whistling a second-minute shot wide.
Cardiff, the lowest scorers in the Championship with 20 goals in 26 games, had not scored in nearly six hours of football.
But their goal drought ended on 348 minutes when Mark Harris broke behind the dozing Pascal Struijk to force a save from the advancing Joel Robles.
The ball broke to Isaak Davies and, although his effort was blocked, it squirted to Philogene who made no mistake from six yards.
Cardiff doubled their lead seven minutes later just after the half-hour mark.
This time Ojo was left unattended from Andy Rinomhota’s floated pass and Robles was beaten again by a fine finish into the roof of the net.
Gnonto was booked for simulation, a sign that Leeds frustration was growing, before the young Italian was off target with a wayward header.
Marsch waited until nearly 15 minutes of the second half to make his first substitutions, a triple change.
Midweek recruit Max Wober, Rodrigo and Cody Drameh – the reigning Cardiff player of the year following his loan spell in south Wales last season – were sent on to rescue the situation.
The move almost paid off instantly as Struijk headed wide when it appeared easier to score.
But Leeds halved the deficit after 65 minutes, Rodrigo meeting Sam Greenwood’s clipped cross with a close-range header that Jak Alnwick got a strong hand to but was unable to keep out.
Leeds set up camp in the Cardiff half and won a spot-kick 10 minutes from time when Bagan dived to tip Junior Firpo’s goalbound shot around a post.
Alnwick guessed correctly to his right to push away Rodrigo’s kick but 18-year-old Perkins, who had only been on the pitch eight minutes, secured an Elland Road replay.