The defeat means Puel's men have now picked up just a single point from their past five games, with the pressure on the Frenchman increasing as they stay in 12th place.
Puel has reportedly lost the support of several influential players, including England striker Vardy, who was left on the bench for the first 60 minutes before coming on to miss a penalty with his first touch.
Christian Eriksen netted moments later and although Vardy got one back, Son Heung-min's late strike ensured third-placed Tottenham the victory.
Son was booked in the first half after going down in the area under a challenge from Harry Maguire, becoming the fourth Spurs player to be yellow-carded for simulation this season. 'Unbelievable. When you compare with the penalty against us, unbelievable. The problem is, I told Michael Oliver, the situation of Liverpool in the last minute that should be a penalty, but it was a clear penalty.
This gritty success was the ideal preparation for hosting Borussia Dortmund in the Champions League last 16 first leg on Wednesday. "We are nice people".
"If we are being targeted (by referees), I don't understand why".
A statement said the club are undergoing "remedial works on the safety systems" before they could move forward to the final stages of testing, leaving the door open to the possibility that Spurs could play their remaining home games at Wembley this season. Davinson Sanchez had scored his first goal for Tottenham to give...
Mauricio Pochettino's side took the lead through Sanchez's first half header, but they were indebted to Lloris for keeping out Jamie Vardy's spot-kick after the interval at Wembley. I said if he felt good he could take it. "Unbelievable, unbelievable, unbelievable", Pochettino said.
Three minutes later the game took another twist as we doubled our lead when Oliver Skipp - on his second Premier League start - closed down a clearance, Llorente picked up the loose ball and laid it off for Eriksen, who drilled in right-footed from 20 yards.
Vardy gave Leicester hope in the 76th minute, pouncing from close-range to convert Pereira's cross in typically predatory fashion.