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The Foxes' dream of completing their surreal journey from 5000-1 no-hopers to English champions felt more tantalisingly real after 10 minutes when Ashley Williams's careless clearance gifted Riyad Mahrez his 17th goal of the season.
Ulloa, filling in for Leicester's suspended top scorer Jamie Vardy, then took centre stage. He headed home the second and tapped in a third on the hour as the Foxes cruised while their fans merrily sang: "Are you watching, Tottenham?"
The Spurs faithful who were watching could only sigh as substitute Marc Albrighton smashed in a fourth in the dying minutes to confirm Leicester's eight-point lead over the second-placed Londoners.
Should Tottenham lose their game in hand at home to West Bromwich Albion on Monday, the Foxes, who need five points from their last three games to take the title, could even be crowned champions next Sunday with victory at Manchester United.
"I told them we have a dream and now we have to fight to make a dream reality," Leicester manager Claudio Ranieri said.
On such a nerve-racking afternoon for his side, playing for the first time in 45 matches without talisman Vardy in their starting lineup, an early settler was required yet few imagined Swansea captain Williams would be the one to provide it.
Under no pressure on the edge of his own box, he picked out a surprised Mahrez with a lazy clearance and, though there was a suspicion of handball from the Algerian, he finished brilliantly, shaping to curl a left-footer into the far corner but instead beating Lukasz Fabianski at his near post.
It signalled a return to his best from Mahrez after a recent slight drop from the peaks of his dazzling season which makes him the favourite to lift the Professional Footballers' Association player of the year award later on Sunday.
Ulloa, Leicester's then record 8 million-pound ($11.5 million) signing when he joined in 2014, had not started a game since January but with Vardy serving at least a one-match ban following his sending-off against West Ham United, the Argentine was in the mood to remind everyone again of his threat.
When Danny Drinkwater delivered a fine free kick from wide on the left, Ulloa beat the unfortunate Williams to head into the corner and, after a persistent run and cross by Jeffrey Schlupp on the hour, he slid in the third from close range.
Ulloa received a rapturous ovation after he came off with a back injury but the King Power, by now in full party mode, could celebrate one final goal after Albrighton followed up fine work from substitute Demarai Gray to hammer in from close range five minutes from time.
As the pressure has increased on them, Leicester have just kept delivering, whether it be through unsung squad players like Schlupp and Ulloa or stars like Mahrez, who, according to Ranieri, was the Foxes' "light".
"Yes, I felt it a little bit," conceded Mahrez, when asked if he felt pressure to deliver in Vardy's absence. "But in this team, we don't just need one player. It's about the team spirit."
It is a spirit -- and organisation -- which has now seen them remain unbeaten in their last 14 home matches and keep 12 clean sheets in their last 17 league games.
"We needed this win because it's closer now," said Mahrez before flying off with his team mates by helicopter to the PFA Awards celebrations in London.
"Eight points clear, three to play, we have everything in our hands."