Luton started life under new boss Paul Buckle by beating Hayes and Yeading to keep up their play-off hopes.
Stuart Fleetwood fired home Jake Howells's cross to put the hosts ahead, before Daniel Wishart tapped in an equaliser from six yards out.
Fleetwood's superb volley then restored the lead, and Keith Keane poked home another Howells cross for 3-1.
Hatters defender Janos Kovacs turned the ball past his own keeper, but Andre Gray rounded it off with a fine strike.
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Luton Town manager Paul Buckle told BBC Three Counties Radio:
"If your strikers are on the front foot looking to shut down you've always got a chance.
"Both centre-forwards took that on board. We did change early in the second-half because we couldn't match up.
"So we paid respect to their system but I thought it worked really well.
"We've got to defend the box a lot better. But I think that comes from feeling a bit sorry for yourself."