Tom Davies gaves the hosts the lead in the first minute but Islam Slimani had Leicester back on level terms soon after.
Besides that Everton-Bournemouth game, there was one other match with nine goals this season: Swansea's incredible 5-4 win over Crystal Palace, which featured seven goals in the second half.
Lukaku notched for the eighth straight home game to level before Phil Jagielka brought a breathless first 45 minutes of play to an end with a header to restore the Blues' advantage.
"The team selection was with the games coming up in mind", Shakespeare said.
That grit comes from the same place that saw Mirallas lose his temper with Huth which usually isn't something you want to see from your players, but in a game so unpredictable with 3 goals in 9 minutes, it is precisely the kind of ferocity Everton needed.
The game's sixth goal was not far away, though, and it turned out to be Everton's fourth.
Leicester City manager Craig Shakespeare said Sunday's 4-2 loss at Everton, his first defeat since taking over from Claudio Ranieri, would not affect his squad as they prepare for a Champions League quarter-final against Atletico Madrid.
After that, Barkley was sent clear as Leighton Baines won the ball 40 yards out and went round Schmeichel, who recovered superbly to block as the midfielder looked set to find an empty net. Leicester failed to mark efficiently and Jagielka was gifted with a free header to guide Mirallas' corner into the top corner.
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One goal in 30 seconds, three inside 10 minutes and five before the half was out. Subs: Mahrez 6, Musa 5, Ulloa 6.
This worked effectively when the foxes' scored an equaliser on the 4th-minute but Everton maintained possession and Leicester became tired due to their persistent and relentless attempts at closing down.
"We have played together for a long time", said Lukaku.
"We spoke a lot about Ross and Rom because they are really important, most of the time the quality of the players can be the difference between Everton and the opponent".
We've got a strong squad and I believe in all of them.
So, too, did Everton as a collective and it's the fortitude of will combined with the matching strength of the players who drove the side on to victory that was so pleasing to witness.
Lukaku maintained his run of scoring in every home match in 2017, a streak he extended to eight games as he took his Premier League tally to 23 goals, one more than Middlesbrough's total for the entire season.