Late goal seals Town's cup progress
Away at Leicestershire Senior League Premier Division Friar Lane and Epworth it looked as if the two sides could not be separated deep into the second half.
But Burniston had other ideas, scoring the only goal of the contest in the 78th minute.
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Hide AdThe finish to ensured Melton’s progress into the third round of the county competition.
Town will return to cup action next Wednesday evening, their next contest.
They travel to Lincolnshire to face United Counties League Premier Division outfit Holbeach United in the UCL Knockout Cup.
Kick off at Carter’s Park will be at 7.45pm.
Saturday’s postponed fixture at Rushden and Higham United will now take place on Wednesday, November 14.