Gillingham retained top spot in League Two despite suffering a shock 1-0 home defeat at the hands of Grimsby.
The Mariners secured their second win on the road in the space of four days as Kieran Green grabbed the only goal of the game.
The hosts started the brighter of the two teams but Priestfield was silenced on 21 minutes when Green fired beyond the reach of Glenn Morris after being played through on goal by Denver Hume.
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The visitors defended resolutely, limiting Mark Bonner's men to very few chances.
However, the Gills should have levelled matters just before the hour mark but Elliott Nevitt was unable to turn Jayden Clarke's cross home from close range.
Gillingham dominated possession in their search for an equaliser but were unable to break down a gutsy Grimsby side.
In the closing stages substitute Tim Dieng went close for the hosts, but on the stretch his effort from a few yards out was guided narrowly wide.