Asa Hall's early strike made it three straight wins for promotion-chasing Luton as they maintained their push for a Blue Square Premier play-off spot.
Hall hit a low 25-yard shot into the bottom left-hand corner after just nine minutes to secure the three points.
Eastbourne's Joe Benjamin then saw his effort just miss Mark Tyler's post.
The home side came out stronger in the second-half, but were unable to convert possession into chances, ensuring Luton a fifth win in six league games.
Hall's strike, his sixth of the season, leaves Richard Money's Hatters in fifth, two points ahead of nearest challengers Mansfield Town with three games in hand.
Eastbourne almost drew level immediately, when Town keeper Tyler made an excellent save to keep out Marc Pullan's close-range strike.
But Hall nearly doubled his side's lead with a cross-shot saved by home keeper Danny Knowles, who also denied Tom Craddock.
Craddock spurned another opportunity when well placed. But Borough rarely looked like forcing an equaliser, leaving Luton to hold on for a deserved three points.
Defeats for both Barrow and Forest Green ensure that Eastbourne remain in 19th - just three points clear of trouble.
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