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Striker James Alabi opened his Dover account as Whites retained their position at the top of the National League on Saturday.
Alabi's 32nd minute header was all that separated the sides at half-time but Whites comfortably wrapped up a fourth victory in five home matches with a second goal just before the hour from defender Connor Essam.
The win, Dover's sixth in seventh matches against the Spitfires, extended their unbeaten league run to nine and moved them a point clear at the top from Macclesfield. They had started the day as leaders but only ahead of Wrexham on goal difference.
After a relatively quiet opening Dover's Nortei Nortey had the first shot on target after 11 minutes though his 20-yard drive failed to extend Eastleigh's former Whites keeper Ross Flitney.
Whites skipper Mitch Brundle went close midway through the half with a 20-yard effort that bounced just wide and immediately at the other end home keeper Mitch Walker did well to clutch a Mark Yeates free-kick which had taken a slight deflection on its way through.
Dover then began to step up the pace and the breakthrough came on 32 minutes when Eastleigh failed to clear Mitch Pinnock's long throw and Alabi - on loan from Tranmere - headed home after his first effort had been blocked.
Almost immediately a cross from Josh Passley drifted just wide of the far post and then Whites top scorer Ryan Bird got up well but could only direct his header over.
Whites were well on top at this stage with Brundle finishing a neat move by firing wide from the edge of the box, but they had a warning shot on 41 minutes when an error by Femi Ilesanmi gave Ben Williamson a clear sight of goal but Walker got down well to his low to left to save.
Bird then tested Flitney at the other end and Whites carried that momentun into the second half with Nortey's shot from the edge of the area being deflected over in the opening seconds.
Alabi almost then grabbed his second powering his way through only for Flitney to save well with his legs but Whites did not have to wait much longer for their second as Essam struck on 57 minutes.
His initial downward header from Brundle's hanging corner was kept out but he reacted quickly to stab home the rebound to claim his first goal of the season.
Eastleigh rang the changes by throwing on three substitutes in the space of three minutes but they seldom looked like pulling a goal back and Dover almost struck again on 70 minutes.
The impressive Nortey finished a fine run with a cross to the far post where Alabi, straining to reach the ball, lifted his shot over.
That was Alabi's final contribution before being replaced by Kadell Daniel but he could look back with satisfaction on his best performance in a Dover shirt.
Whites could have added to their tally in the final 10 minutes with Femi Ilesanmi squandering the best chance when he fired wide after a well-timed run into the box.
Eastleigh almost grabbed a consolation in the final minute of normal time when Walker made a fine tip over save from Callum Howe.
Dover: Walker, Passley, Ilesanmi, Gallifuoco, Parry, Essam, Brundle, Pinnock, Nortey, Bird, Alabi (Daniel 72mins); Subs: Richards, Fazakerley, Okosieme, Deen-Conteh.
Eastleigh: Flitney, Hoyte, Constable (McAllister 65mins), Yeates, Hollands (Matthews 62mins), Boyce, Miley, Williamson, Howe, McSheffrey (Strevens 62mins), Shaw; Subs: Zebroski, Read.
Attendance: 1273.