For the Club's Remembrance Fixture, the Frenchman made seven changes to the side that beat Leeds United on Tuesday, deploying a 4-2-3-1 stratagem against the Merseyside outfit at King Power Stadium.
Puel’s men were rampant in the first half as Gray, Wes Morgan and Ben Chilwell all went close inside the opening 10 minutes.
The Foxes’ first goal came not long after, courtesy of a stunning run from Gray. He sprinted with the ball from inside his own half and surged past the Everton midfield before offloading to Riyad Mahrez – the Algerian calmly squared to Vardy to fire home for 1-0.
Mahrez had an effort saved by Jordan Pickford shortly after, while at the other end, Dominic Calvert-Lewin missed a big chance to equalise, but couldn’t connect with Aaron Lennon’s cross.
A stroke of luck saw the Foxes double their lead just before the half-hour mark. Jonjoe Kenny attempted to clear Gray’s cross, but sliced the ball into his own net past Pickford.
Two attempts from Kevin Mirallas came just before the break. The first flew wide, while Kasper Schmeichel had to get down low to tip the second behind as Everton put the hosts under pressure.
A spell of defending for City followed after the interval, with the Leicester back line standing strong on a number of occasions to halt the Toffees attack.
Everton continued to flow forward but Puel’s outfit matched them and looked dangerous on the break. With four minutes to go, Vicente Iborra played a one-two with Vardy, only for the impressive Spanish midfielder to poke wide from inside the area.
Toffees left back Leighton Baines hammered a half-volley towards goal with a minute to play, but Schmeichel watched the strike fly harmlessly over the bar.
Major moment
A rampant start to the game yielded numerous goalscoring opportunities for Leicester City and it was only a matter of time before they would take one of them.
The build-up to the goal was brilliant and Demarai Gray deserves plenty of credit for his role in it. He ran from his own half to play in Riyad Mahrez, who teed up Jamie Vardy for the opener.
Vardy’s strike set the tone in the first period and while Everton were much-improved after the break, they couldn’t breach City’s solid defensive unit.
Who impressed?
Demarai Gray put in an excellent all-round performance against Everton. He showed lethal pace on the break and put in a good defensive shift to help City maintain their 2-0 lead in the second half.
However fortunate his goal may have been, Gray certainly deserved to get on the scoresheet following his contribution on Sunday.
Where do we stand?
A second straight Premier League victory for Leicester City sees them move up to 11th position in the table, four points off the bottom three.
Coming up…
A trip to Stoke City is next up for the Foxes, as they head to the bet365 Stadium on Saturday 4 November (12:30pm kick-off) ahead of the final international break of 2017.