Victory against arch-rivals AFC Totton next Saturday will guarantee BAT a top-eight finish following their 4-1 success at Alton Town.
All the goals came in the second half with Richie Gregory firing the Tobaccomen into a 55th-minute lead. Alton levelled on the hour only for Matt Czaska to beat two defenders and restore BAT's lead just moments later.
Gregory picked out Dean Platt to notch their third after 70 minutes with Phil Walsh crossing for Lloyd Jenvey to head in a fourth ten minutes from time.
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