Dominic Calvert-Lewin sent Everton ahead from the penalty spot in the 24th minute, before Elijah Adebayo levelled the scores seven minutes later, and it finished all square in Luton.
The result has left Rob Edwards's side in 18th spot in the table, level on points (26) with 17th-placed Nottingham Forest, who now have a game in hand, while Everton stay 15th, moving onto 37 points from their 36 matches.
Luton will finish their campaign with matches against West Ham United (A) and Fulham (H), and it does appear that the race to remain in the division will go to the wire, with Burnley just two points behind in 19th and also now having a game in hand on the Hatters.
Luton could drop to 19th heading into gameweek 37
Teden Mengi was perhaps a touch fortunate not to concede a penalty in the 16th minute for a challenge on Dwight McNeil, but shortly after, the Luton centre-back was penalised for a needless foul on Jarrad Branthwaite after a corner had been delivered into the home side's penalty box.
The referee was sent across to the monitor following advice from VAR, and it was no surprise when he pointed to the spot; Calvert-Lewin stepped up the Toffees, and he managed to fire his effort past Luton goalkeeper Thomas Kaminski, who got one leg on the ball, to put the Merseyside giants ahead.
However, retreating into their shell has not been the Luton way this season, and it will not be for as long as Edwards is at the helm.
The home side's leveller came in the 31st minute, with Adebayo proving to be too big and too strong for Ashley Young at the far post, the striker collecting a cross from Albert Sambi Lokonga before firing past Jordan Pickford and into the bottom corner.
There was a check for a possible foul on Young, but it was deemed to be a fair challenge.
Abebayo now has 10 Premier League goals to his name this season, and his total is even more impressive considering that he was out between the middle of February and the end of April through injury; Luton will do well to keep him this summer if they are relegated.
Elijah Adebayo makes it 10 Premier League goals for the season
Everton dominated the possession towards the end of the first period, but the two teams went in level, with a huge second 45 minutes of Premier League football to come at Kenilworth Road.
Gabriel Osho sent one just wide of the Everton post early in the second half, before Ross Barkley headed over the crossbar, with Luton doing all of the pushing on home soil.
Everton remained a threat, though, with Kaminski making a brilliant save to keep out a speculative effort from Jack Harrison, who was the away side's most threatening player for long spells.
Kaminski made another stunning stop in the 77th minute to keep out a header from Calvert-Lewin, before Luke Berry was denied twice late on, once by Pickford and once by an Everton defender, and Branthwaite then did brilliantly to turn an Andros Townsend effort wide of the post.
There were ultimately no more goals at Kenilworth Road, though, with Luton being made to settle for a point, and they will now be looking for favours elsewhere when it comes to their battle to stay in the division.