Everton secured only their third win in 13 Premier League matches with ease, after second half goals from Kevin Mirallas and Romelu Lukaku, to leave Leicester only three points above the relegation zone
But they capitalised on poor defending from the home team to secure an instant response after their cruel late defeat to Liverpool in their last game.
Vardy’s suspension, for a two-footed challenge on Stoke’s Mame Biram Diouf, and the rejected appeal have infuriated the Leicester hierarchy and masks with the England international’s face on them were handed out before kick-off.
Yet if this was meant to be sticking two fingers up at the governing body, with FA chairman Greg Clarke present at the game, Vardy’s team-mates were unable to join in after a poor, disjointed performance.
Claudio Ranieri had thought the dramatic 2-2 draw at Stoke in their last game would act as the turning point in their season but Leicester are going in reverse towards the bottom three.
Ranieri said: “It is difficult to say how much we missed Jamie but we are very sad as we wanted to give our fans a good present. I didn't see the masks.
“This season is up and down, after something good there always seems to be a setback. In the first six months of 2016, everything was right and now everything is wrong.
After an insipid opening half Everton took the lead six minutes into the second period, after an alarmingly simple goal that will have infuriated Ranieri.
Joel Robles’ mammoth clearance somehow cannoned its way through Leicester’s midfield and defence to send Mirallas clear on goal.
The Belgian eluded Wes Morgan to run into the area and his low shot took a deflection off Marcin Wasilewski to loop over Kasper Schmeichel.
With Leicester lumbering, Ranieri introduced Riyad Mahrez and Leonardo Ulloa with 25 minutes left to play and it produced a response.
Ulloa headed straight at Robles and at last Leicester finally roused themselves, but there was to be no dramatic repeat of their finish at the bet365 Stadium.
Everton missed a wonderful chance to increase their lead in the 83rd minute, with Idrissa Gueye somehow scooping Lukaku’s cross over the bar from six yards.
Yet Lukaku broke clear in added time, outmuscling Morgan, to advance into the area and slide the ball into the corner. This was Everton’s first away win since September and their first at Leicester since December 1997.
Koeman said: “It’s always important to win because everybody knows our away performances in the last 2 or 3 months have not been good.
“A clean sheet will be good for our confidence and we won all the battles in the second half.”