A first-half goal from Croydon mid-fielder, James Greenaway was all that separated these two sides, at the end of a close, often ill-tempered contest at Calthorpe Park.
Greenaway's strike in the 28th minute, following a corner, capped a good first half by the visitors, who deserved their lead going into the interval.
For their part, Fleet created few chances, although wingman, Tinoi Christie could have scored after only 3 minutes, but his shot was well-blocked by Croydon keeper, Robert Frankland.
Croydon looked the more threatening side in the first half, with James Evans hitting the post early on, and Greenaway shooting wide from a good position, again following a corner.
After the break, Fleet fought back well, and despite losing Andy Sinton with a shoulder injury just before the break, began to press well, and soon Frankland had plenty to do, saving well from Fleet striker, David OcQuaye, and again from Christie.
At the other end, Fleet keeper, Justin Gray did well to turn a well-struck free-kick by Evans round the post on 50 minutes. But in the end, the Fleet side could not turn their possession into goals, and the visitors left with all three points.