The Spitfires made it five in a row in all competitions at the Dripping Pan (Lewes) on Saturday.
Ian Baird continued with his 4-5-1 formation and it paid off with a 4 -1 away win.
Eastleigh took the lead after a uneventful opening 30 minutes with both clubs only having a couple of chances on goal.
Danny Smith opened the scoring with a header that flew into the Lewes net and Eastleigh never looked back after that.
Ten minutes later Brett Williams got his name on the scoresheet when the centre forward turned a shot on goal to put the Spitfires 2 -0 up.
Brett Williams nearly scored again five minutes later but was denied a flick on goal by a goal line clearance.
Half Time: Lewes 0 – 2 Eastleigh
The second half started brightly with chances going the Spitfires way and Brett Williams got his name on the score sheet again with a deflected shot on goal in the 60th minute.
Five minutes later former Lewes man Peter Adeniyi set up Tony Taggart to skid across goal to score Eastleigh’s fourth.
Tom Murphy got the home side a consolation goal on the 72nd minute, the striker took round Gareth Barfoot to score in an Eastleigh net but the damage was done by then and The Spitfires claimed all three points.
Eastleigh are still 8th in the Blue Square Bet South and only one point away from the Play-offs and five points away from the lead – as Braintree did not play today.