Leicester called for offside, but their protests were in vain as Sanchez launched himself into a diving header that flashed past Schmeichel.
Since a very well managed and earned win against Everton at Goodison Park on New Year's Day, it has all gone downhill for the Foxes, bringing Claude Puel back into the red zone where he stood before he casually derailed Chelsea and Manchester City's respective Premier League campaigns.
Tottenham Hotspur warmed up for their Champions League tie against Borussia Dortmund in midweek by beating Leicester City 3-1 at Wembley Stadium on Sunday afternoon, and after the match the praise poured in for their star of the show.
Tottenham kept pressing and were rewarded with a well-worked 33rd minute opener. We won but against a bigger side we couldn't have won that type of game.
Vardy did give the visitors hope when he struck in the 76th minute, but Heung-Min Son grabbed a third for Tottenham at the death.More news: Soundarya Rajinikanth and Vishagan Vanangamudi's glittery wedding in Chennai
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The north Londoners are five points off the top of the table as they try to catch pace-setters Liverpool and Manchester City.
Pochettino says Tottenham and the other Premier League teams in Europe are already at a disadvantage because of the winter breaks given to German, Italian and Spanish teams.
But Lloris stepped up when it mattered most with an excellent save, a pivotal moment as we went 2-0 up minutes later, giving ourselves a platform to go on and win the game. "The way we conceded [chances] is more than we usually concede but I think the victory's fair".
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 the penalty with his first touch. It was a game in our hands, and we had a lot of chances and created a lot of good moves. "I said to him if he felt OK he can take the penalty, but it's not just the penalty that cost us".
While Tottenham are still outsiders to win their first English title since 1961, their ability to stay in contention, despite injuries to key players Harry Kane and Dele Alli suggests they shouldn't be completely written off.