Danny Hylton's header cancelled out Jake Taylor's opener as the Hatters drew for the fourth time in six games.
The visitors went close after 15 minutes when Reuben Reid forced Matt Macey into a save at his near post.
Luton threatened sporadically in the opening half hour, Jonathan Smith volleying over and Jordan Cook narrowly missing the target with a 30-yard free kick.
Exeter goalkeeper Bobby Olejnik made a fine save to keep out Jack Marriott's header, before Hylton missed the follow-up.
After the break, Reid's close-range shot was blocked by defender Alan Sheehan with the striker then firing woefully over the top from eight yards.
The visitors took the lead just before the hour mark when Jack Stacey teed-up Jake Taylor to calmly beat Macey.
Luton pressed for an equaliser and after Ollie Palmer saw his effort cleared off the line by Luke Croll, the substitute crossed for Hylton to power a header home in the 68th minute.
Hylton had an effort ruled out for offside, while Macey denied Ollie Watkins at the other end as neither side were able to find a winner.