Luton took the lead in the 55th minute through a header from Jacob Brown. Plymouth responded in the 70th minute when Maksym Talovierov rose to meet a deep cross and powered a header into the far post, securing a draw.
Luton had chances early on, including a close header by Lasse Nordås from an Alfie Doughty cross that just missed. Plymouth had a disallowed goal in the first half when Callum Wright put the ball in the net, but he was flagged offside.
Both teams continued to press after the equaliser. Luton had a few opportunities from set pieces late on, but Plymouth defended well and held on for a point.