A 28th-minute Leon Legge strike and second-half Deon Burton penalty gave Gills a crucial win at the Priestfield Stadium.
Meanwhile at Vale Park, Morecambe striker Lewis Alessandra was the difference between the sides with a 63rd--minute goal.
Burton Albion went into the third automatic promotion spot with a 4-0 pasting of Fleetwood Town at their Highbury Stadium home thanks to a stunning second-half performance. After the break Congolese Jacques Maghoma hitting a brace - one from the penalty spot - and Bill Kee and Calvin Zola were also on target.
Cheltenham Town were held 1-1 by Aldershot Town at Whaddon Road, with on-loan home forward Paul Benson equalising Danny Rose's first-half opener in the second period. They drop one place and are level with Burton on 53 points.
A point behind are Exeter - winners at home to Accrington Stanley on Friday night - and Rotherham, who won a local derby at home to Chesterfield 1-0 thanks to Johnny Mullins. Northampton Town won 2-1 at Southend United to stay a point further back.
AFC Wimbledon stay bottom despite a 2-1 win over League Cup finalists Bradford City - they are now level on points with Aldershot and one from safety.
In games involving sides in the bottom half of the table Oxford United won 1-0 at Plymouth Argyle, Bristol Rovers were 1-0 victory over Wycombe Wanderers at the Memorial Stadium, Rochdale beat Torquay United 1-0 at Spotland and Barnet triumphed 2-1 at York.
Stanley are third-bottom, level on points with Argyle.