Villa had looked in complete control thanks to Ollie Watkins’ first-half double and it seemed as if they would go on to increase their lead.
England striker Watkins headed in from Leon Bailey’s corner to give Villa the lead and raced onto Douglas Luiz’s ball over the top before slotting in their second.
That one was initially disallowed by the officials for offside but awarded after a video assistant referee review.
Luton, who did not have a shot until first-half injury time, looked like a new team after the break.
Tahith Chong gave them hope with a goal after a scramble in the box and Carlton Morris’ controlled volley from Alfie Doughty’s free-kick levelled the score.
Morris even had a chance to win the game for Luton but his header was straight at Emiliano Martinez.
And Digne made them pay when he headed in a cross from fellow substitute Moussa Diaby.
