Representatives from the Toffees’ prospective new owners 777 Partners were in attendance after back-to-back wins over Brentford and Aston Villa had fostered hopes of brighter days ahead.
But set-piece goals from Tom Lockyer and Carlton Morris put Luton two up and, although Dominic Calvert-Lewin pulled one back before half-time, the Toffees could not find an equaliser.
Instead it was a landmark day for Luton, who celebrated their first top-flight victory since a 2-0 success against Aston Villa in April 1992.
Everton began the match very much on the front foot but, as with previous games at Goodison this season, they could not turn chances into goals, or even trouble Thomas Kaminski.
Dwight McNeil had the first opening in the third minute, volleying just past a post after a defensive slip, while James Garner, Idrissa Gueye and Amadou Onana all put their efforts wide and Calvert-Lewin, back in the starting line-up after goals in successive matches, headed straight at the keeper.
Luton’s only opening had been a shot from Marvelous Nakamba that flew high and wide, but they looked dangerous from set-pieces and Lockyer gave notice of his threat by finding space in the middle of the box from a corner and heading just over the bar.
And it was the Luton captain who made the breakthrough from another corner in the 24th minute.
Morris’ powerful header hit the bar and rebounded off Jordan Pickford, Ashley Young was too slow in trying to clear the ball and Lockyer got in the way to divert it into an empty net.
The optimism around Goodison Park rapidly drained away and things got worse in the 31st minute when Morris was given space at the back post to meet Alfie Doughty’s free-kick and send a crisp volley flying into the far corner.
Everton should have pulled one back six minutes later when McNeil’s well-judged cross found Garner unmarked six yards out, but his header hit the angle of post and bar.
Four minutes later they did manage to put the ball in the back of the net and it was eventually given after a three-minute VAR check.
Garner’s ball in found Onana, who appeared to be having his shirt pulled by Reece Burke as he scrambled a shot, which was blocked by Kaminski.
With Everton fans screaming for a penalty, the ball squirmed away from the keeper and Abdoulaye Doucoure teed up Calvert-Lewin, who was eventually deemed to be just onside, for the simplest of finishes.
Luton dug in to preserve their lead until half-time and both teams made changes for the second half, Jack Harrison replacing Gueye for his league debut for Everton and Mads Andersen coming on for Burke.
The Hatters then lost captain Lockyer to injury, with Teden Mengi coming on in his place.
There was a big cheer when Beto was introduced for Everton, who could manage little more than lofting hopeful balls into the box as they sought the equaliser.
Luton had the ball in the net again with 63 minutes gone but Morris was denied his second by an offside flag.
Everton slowly began to ramp up the pressure, but Kaminski did not have a save to make in the second half, with Beto heading over from the best two openings, and boos greeted the final whistle.