Tyson struck in the 67th minute to deny the relegated Hatters a point from a spirited display.
Forest laboured for the most part but Tyson punished Luton for failing to clear a Chris Cohen cross when he forced the ball home from close range.
Until then it looked as though Colin Calderwood’s side would be faced with a frustrating afternoon with Luton keeper Dean Brill dealing with all that Forest had to offer.
He saved early on from Kris Commons and then saw defender Sol Davis clear off the line from skipper Ian Breckin after the corner that followed.
And after Tyson had given Forest the breakthrough, Brill saved spectacularly from Wes Morgan’s header following a corner by substitute Lewis McGugan.