Brian Okwera headed home an Abs Seymour cross to score what proved to be the only goal of the game after 19 minutes.
Wroxham`s Jackson Ramm came close to levelling on 38 minutes with a 30-yard effort that hit the top off the crossbar. And the Yachtsmen threw everything at the Millers in the final quarter but weren`t able to find a leveller.
The result left the Yachtsmen a point ahead of third-bottom Heybridge Swifts, who now have a game in hand.
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