The Premier League new boys started their pre-season schedule with a 6-1 demolition of Ilkeston on Tuesday and Nigel Pearson's men followed up with another win at the Supachalasai Stadium in Bangkok.
Everton had the better of a close first half, but Leicester - who handed a start to new signing Leonardo Ulloa - saw David Nugent have a goal ruled out.
And the East Midlands outfit continued to improve following the break and were rewarded just after the hour mark when Taylor-Fletcher finished from close range after good work from Jamie Vardy.
It was Everton who settled quickest into the game and Luke Garbutt was the first to test Kasper Schmeichel with a free-kick from the edge of the area that was well saved by the Dane.
Schmeichel remained the busier of the two goalkeepers and had to be on hand to make a fine stop from Leon Osman's driven shot.
However, Leicester grew into the match and Nugent shot narrowly wide before soon after he rifled past Joel Robles only to be denied by the offside flag.
The lively Vardy - who was one of several Leicester changes at the break - was looking particularly dangerous, and it was he who helped the newly promoted side break the deadlock in the 66th minute.
He beat the onrushing Joel to the ball before keeping his composure and squaring into the path of Taylor-Fletcher who tapped home.
Riyad Mahrez then curled wide 10 minutes from time but one goal proved to be enough for Leicester.
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