Trying to recover from Tuesday's 2-0 defeat by leaders Oxford, they could have led in 70 seconds but Tom Craddock's header hit the post.
Town took the lead with Adam Newton's finish from outside the box and only a fine Tim Deasy save prevented Craddock from making it 2-0.
Deasy then frustrated Kevin Gallen as Town tried to seal the game early.
Luton: Tyler, Gnakpa (Hatch 75), White, Pilkington, Murray, Hall, Keane, Jarvis, Craddock, Gallen, Newton. Subs Not Used: Gore, Blackett, Basham, Howells.
Booked: Craddock, Hall, Hatch.
Goals: Newton 21.
Barrow: Deasy, Spender, Dugdale, Bolland, Pearson, Rutherford, Bond, Boyd (Hulbert 63), Logan (Taylor 89), Shaw (Rogan 67), Walker. Subs Not Used: Tomlinson, Jones.
Booked: Bolland.
Att: 6,264
Ref: W Barratt (Halesowen).
Source: BBC Sport
Source: BBC Sport