Leeds survived an FA Cup third-round scare as Sonny Perkins' stoppage-time equaliser secured a 2-2 draw at against 10-man Cardiff City.
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, England U19 international Perkins squeezed home from close range three minutes into injury time.
- Cardiff or Leeds to face Boreham Wood or Accrington
- FA Cup fourth-round draw in full
- How the teams lined up | Match stats
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How Leeds fought back to earn a replay...
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.
Cardiff, the lowest scorers in the Championship with 20 goals in 26 games, had not found the back of the net in nearly six hours of football. But their goal drought ended on 24 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.
Signs of Leeds' growing frustration became apparent, with Wilfried Gnonto booked for simulation before the young Italian was off target with a wayward header.
Jesse Marsch waited until just shy of the hour mark 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 and reignite Cardiff's hopes of a Premier League scalp.
However the visitors continued to push, and Leeds forced a replay deep into stoppage time when 18-year-old Perkins, who had only been on the pitch eight minutes, got in front of Alnwick to poke home Junior Firpo's flick.
What the managers said...
Leeds boss Jesse Marsch: "The whole first half we were not in sync and not aggressive enough. We didn't have a full understanding of what this tournament and this game was going to require.
"We need better tactical understanding and savviness and awareness for exactly what matches require.
"We know there's an opportunity back at Elland Road with the draw, and everything is laid out in front of us.
"If we learned one thing is that if you don't show up and you're not ready to play from the beginning, you're going to cause yourself problems."
Cardiff boss Mark Hudson: "First and foremost, the overriding feeling is I'm proud of the performance we put in against a top Leeds side.
"Tactically, we got it right. We showed a good shape. We countered when we could, we frustrated them. We scored two really good goals.
"We knew we would suffer in the second half. They have got an abundance of talent to come off the bench.
"It's not bad when you can bring Rodrigo off the bench."
FA Cup fourth-round draw in full
- Preston vs Tottenham
- Southampton vs Blackpool
- Wrexham vs Sheffield United
- Ipswich vs Burnley
- Manchester United vs Reading
- Luton or Wigan vs Grimsby
- Derby vs West Ham
- Stoke vs Stevenage
- Blackburn vs Forest Green or Birmingham
- Walsall vs Leicester
- Sheffield Wednesday vs Fleetwood
- Manchester City vs Oxford or Arsenal
- Bristol City or Swansea vs Chesterfield or West Brom
- Brighton vs Liverpool or Wolves
- Fulham vs Sunderland
- Boreham Wood or Accrington vs Cardiff or Leeds
What's next?
Cardiff's next game is at home against Wigan in the Championship on Saturday January 14; kick-off 3pm.
Meanwhile, Leeds travel to Aston Villa on Friday Night Football, live on Sky Sports; kick-off 8pm.