Oldham had almost total domination at Boundary Park but they could not find a winner after Craig Davies had given them the lead with his tenth goal of the season.
Davies made the breakthrough on 32 minutes but Fojut levelled just two minutes later and Luton hung on despite long spells of pressure by the Latics.
Oldham are also enjoying a good run of form and have not lost any of their last seven matches in League and Cup, but they remain at the wrong end of the table with Luton, whose season was hit by a ten-point deduction for going into administration.
It was a physical contest and both managers were unhappy with the referee after he made several controversial decisions and did not appear to have full control of the game.
The star of the show was Luton keeper Dean Brill, who was the busiest player on the pitch and made a string of saves.
Chances were few and far between in the early stages although Oldham were on top and opened the scoring following a superb throughball from winger Chris Taylor.
Davies sprinted through for a one on one with Brill and rounded the keeper before slotting home from ten yards.
Luton had created virtually nothing but they levelled when David Bell hit a free-kick to the far post and Fojut headed it back across goalkeeper Mark Crossley to score from six yards.
Oldham went on to control the second half but they wasted a number of openings, starting when Lee Hughes sent a header wide.
Stefan Stam was also off target before Brill pulled off a superb save to deny Hughes from close range.
The best chance fell to Gary McDonald but he pulled his six-yard shot inches past the post following Stam's header down.