Vale took a two-goal lead thanks to Tom Pope's header - his 26th goal of the season - and Adam Barrett own goal.
The Gills fought back and scored one through Danny Kedwell's hit from distance, but despite pressure in the dying stages, they could not force an equaliser.
Port Vale, who went into the game two points behind their opponents, now lead the division by a point.
Bradford were brought down to earth with a bump four days after beating Aston Villa in the Capital One Cup when a last-minute penalty earned Oxford a 2-1 win at Valley Parade.
Matt Paterson stepped off the substitutes' bench to clinch a 2-1 win for Burton after they had trailed against Torquay.
Edgar Davids' magic continues to rub off on Barnet as they captured the scalp of another promotion favourite with a comfortable 2-0 victory at Rotherham.
Chesterfield swept aside Northampton with three goals in the space of eight first-half minutes to cruise to a 3-0 win at the Proact Stadium.
Troy Brown and Dani Lopez were on the scoresheet as Aldershot beat Accrington 2-0 for a third successive win to give a their survival hopes a further boost.
Relegation-threatened Bristol Rovers gave their survival bid a major shot in the arm with a shock 3-0 victory away at play-off chasing Fleetwood.
Matt McClure stepped off the substitutes' bench to rescue a point for Wycombe in a 2-2 draw and deny relegation-threatened Wimbledon their third win on the spin.
Exeter recorded their first home win since the start of November with a hard-working 3-0 victory over promotion rivals Southend.
Striker Shaun Harrad ended his goal drought with a wonderful 25-yard strike to hand Cheltenham a share of the points in a 1-1 home draw with York.
Medy Elito was the Dagenham & Redbridge hero as his stoppage-time strike helped his team leapfrog visitors Rochdale in the table with a 2-1 win.
John Sheridan secured his first victory as Plymouth manager with a 2-1 triumph over Morecambe, thanks to two early strikes from Conor Hourihane and Paris Cowan-Hall.