Leeds striker Luke Varney held his nerve after being sent clear by skipper Michael Brown's throughball in the 15th minute to open the scoring, and Tottenham's hopes of a fightback were dealt a blow five minutes after the break when Ross McCormack slammed home a fine second.
Spurs forward Clint Dempsey deftly headed Gareth Bale's excellent cross inside the far post eight minutes later, having earlier spurned a gilt-edged chance to reduce the deficit, but there was no way back for the Londoners.
Leeds, in fact, could have added to their tally with McCormack guilty of two bad misses in either half.
Home defender Lee Peltier then ensured Warnock's side exacted revenge on Spurs for their triumph at Elland Road at the same stage of the competition after a replay in 2010 with a brilliant last-ditch tackle on visiting substitute Jon Obika in stoppage time.
"I'll probably open a bottle of champagne and have a few little tipples," said Warnock, whose side were criticised by fans after the recent league defeat at Barnsley.
"I'm sure I'll be able to do something like that. I might even treat myself to a bag of crisps."
Some Leeds fans are angry at the expected departure of leading goalscorer Luciano Becchio, but Warnock said this display should help lift the gloom.
"We've had negative press on some of the results lately and yet we've won six on the trot at home (now seven)," he said.
"But in Leeds the glass is always half empty, it's never half full in Leeds. That might be a Yorkshire trait."