Andy Arnott stole the points for Dover at New Lodge as his 88th minute strike confirmed back-to-back defeats for Chelmsford.
That was harsh on Paul Parker's men, who had contributed to a passionate if uninspiring clash. The winner came in unfortunate circumstances for home keeper Paul Nichols, who spilt Matt Carruthers' long-range effort straight into the path of Arnott who had the simple task of placing home.
Earlier in the game, Dale Watkins had two half chances to give City the lead, but failed to test Paul Hyde. Mike Rutherford went closer with a brilliant header, but the Dover number one was not to be beaten.
Simon Glover's introduction from the bench offered Dover the width they craved as the game wore on, but neither side created the opportunities until Nichols' late spill.
Dover's third win in four games leaves Chelmsford three points above the relegation places.
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