Sean McConville grabbed a late leveller as Stockport drew for the fifth time in seven Blue Square Premier matches.
Gary Brabin's side led after just five minutes when Alex Lawless drilled in a superb shot from 20 yards out.
McConville then wasted a great chance to draw County level when he shot wide from inside the box.
Dietmar Hamann's side were heading for their second defeat in a week until midfielder McConville smashed home from the edge of the box in injury time.
Striker Stuart Fleetwood almost won it for Luton after coming off the bench for his debut but he hit the post from 18 yards out.
Stockport: Glennon,Blackburn,O'Donnell,Piergianni, Holden (Fraughan 68),McConville,Routledge,McCann (Nolan 77),
Rowe,Chadwick (Elliott 67),German. Subs Not Used: Ormson,Paton.
Goals: McConville 90.
Luton: Tyler,Osano,Antwi,Keane,Asafu-Adjaye,Kissock (Dance 69), Lawless,Watkins,Willmott,Crow (Fleetwood 83),Morgan-Smith.
Subs Not Used: Kevin Pilkington,O'Connor,Carden.
Goals: Lawless 5.
Ref: Robert Merchant (Staffordshire).