Claude Gnakpa netted a late winner as Luton edged the win over Blue Square Bet Premier strugglers Hayes & Yeading.
The Hatters were second-best for most of the match, but Gnakpa's 18-yard strike handed them all three points.
Luton keeper Mark Tyler twice denied Jake Hyde in the first half, and also kept out attempts from Andy Yiadom, Peter Holmes and Charlie Wassmer.
But it was the visitors who broke the deadlock on 75 minutes to leave Hayes languishing in the relegation zone.
Hayes & Yeading: Harrison, Ferrell (McLean 82), Green, Cadmore, Bygrave, Holmes, Pritchard, Yiadom (Appiah 71), Wassmer, Hyde (Wishart 66), Buchanan. Subs Not Used: Deen, Pattison.
Booked: Bygrave, Yiadom.
Luton: Tyler, Gleeson, Pilkington, Kroca, Howells, Gnakpa, Drury, Keane, Crow (Walker 73), Barnes-Homer (Lawless 85), Morgan-Smith.
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Subs Not Used: Hinton, Asafu-Adjaye, Poku.
Goals: Gnakpa 75.
Att: 801
Ref: N Kinsley (Essex).
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