The win puts the undefeated Gills on 22 points while Vale remain one beneath them by goal difference over Exeter and Bradford.
Relegated Exeter were defeated 2-1 at the death by Southend at Roots Hall, while Phil Parkinson’s City continued their fine run with a 2-0 win away to Oxford.
Barnet remain bottom without a win after a 0-0 draw at home to Rotherham, while Bristol Rovers also await their first win of the campaign after a goalless stalemate with Fleetwood.
Dagenham also have yet to take three points from a match in 2012-13, having to fight from two goals down to draw 2-2 at Rochdale.
There were more draws between Northampton and Chesterfield (0-0) and Torquay and Burton (1-1), with York also held without score at home to Cheltenham.
AFC Wimbledon won their first game following the departure of manager Terry Brown as Sammy Moore scored the only goal in a 1-0 win at Wycombe to overtake the Wanderers near the foot of the table.
And Plymouth secured their first away three points of the season with a 3-2 win at Morecambe while Accrington defeated Aldershot 1-0 at home.