Oldham stretched their unbeaten run to seven games but were left to curse two points thrown away at home to Luton.
Latics top scorer Craig Davies gave his side the lead after 32 minutes, when he beat a defender before shooting an angled drive past keeper David Brill.
But Luton equalised two minutes later when Oldham failed to defend a free kick allowing Polish defender Jaroslaw Fojut to head home from close range.
Oldham pressed but Luton hung on and are now unbeaten in six matches.
Oldham: Crossley, Eardley, Trotman, Stam, Bertrand, Allott, Kilkenny, McDonald (Smalley 85), Taylor, Davies, Hughes.
Subs Not Used: Bell, Hazell, Kalala, Wolfenden.
Booked: Kilkenny, Trotman, Hughes.
Goals: Davies 32.
Luton: Brill, Perry, Fojut, Coyne, Jackson, Bell (Currie 82), Robinson, Edwards (Grant 90), Wilson, Andrew (Talbot 73), Furlong.
Subs Not Used: Keane, McVeigh.
Booked: Andrew, Robinson, Furlong, Talbot.
Goals: Fojut 34.
Ref: Andy Haines (Tyne & Wear).