Eastleigh's 1-0 away success at BAT means that the Ten Acres club go into the new year with a seven-point lead.
The only goal came after just three minutes when Warren Kenna crossed to the far post for Robbie Matthews to head home and maintain Eastleigh's unbeaten away record.
Eastleigh's assistant manager David Hughes said: "I'm very pleased because the pitch was heavy and we knew that we wouldn't be able to knock the ball around.
"We all had to dig in and do what I call the ugly stuff well - you've got to put in performances like that if you want to do well."
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