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Ebbsfleet surrendered the lead twice against Thurrock in Blue Square Bet South at Stonebridge Road on Tuesday.
The home side made the perfect start when they scored inside the first two minutes.
Paul Lorraine climbed above the visiting defence to head Ashley Carew’s cross past keeper Joe Woolley.
But Thurrock levelled when David Knight volleyed the ball home after 34 minutes.
Ebbsfleet went back in front two minutes after the break when Tom Phipp got on the end of Carew’s free-kick to score.
However, the visitors replied for a second time on the hour when Craig Pope’s free-kick fell to Kenny Clark and he made no mistake.