Burnham started the match in confident style taking the lead after 12 minutes when Lisa Lory fired home strongly following a good move down the right involving Kate Attreed and Sue Wilson.
The goal stung Dunmow into action and they pinned the home side in their own half for long periods but Nicky Mann was outstanding in the centre of the Burnham defence.
After 25 minutes, Burnham having failed to clear, Dunmow deservedly equalised when the ball was forced home from close range.
This was the first goal Burnham had conceded in over four hours of play.
Just before the interval Burnham regained the lead with the best move of the match. Breaking quickly from defence with long passes, Lory was this time the provider as she crossed from the right for Rachel Hay to open her account for the club with a strong first time shot.
Second half play was largely confined to midfield as both sides struggled to come to terms with the deteriorating wintry conditions but there was a solid performance from Julia Evans who tirelessly supported both attack and defence.
Dunmow finished the stronger as they went all out for an equaliser and Burnham keeper Mel Buckby was forced to make a late double save to ensure maximum points.
Nicky Mann was voted player of the match as Burnham held out to consolidate their league position.
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