The former Rotherham forward handed the visiting side the lead against the run of play when he netted from Charlie Lee's throw-in.
Burton added the second with a solo goal after half-time. Jason Taylor netted for the home side, but Gillingham held on to maintain a five-point lead over second-placed Port Vale.
Chesterfield surged into the top half of the table with a fourth straight league win as they outplayed Port Vale to a comfortable 2-0 success.
Increasing pressure finally paid dividends when Chesterfield debutant Jay O'Shea, on loan from MK Dons, scored in the 37th minute.
The Vale keeper was left stranded in the 64th minute when Richards' cross from the left was deflected to the far post where Tendayi Darikwa headed into an empty net from two yards.
Rochdale slipped to a third straight defeat after Exeter repelled a second-half fightback to leave Spotland with a 3-2 triumph.
Having shipped three first half goals against York in last weekend's 3-2 home defeat, Dale repeated the feat for a second successive match.
The hosts paid the price in the 24th minute when John O'Flynn's header was fortuitously deflected into the path of Pat Baldwin, who stroked the ball past Josh Lillis from eight yards.
Three minutes late it was 2-0. There was more than a hint of offside when Jamie Cureton collected the ball on the right and crossed for O'Flynn to convert from close range, Rochdale's protestations to referee Jeremy Simpson dismissed out of hand.
Exeter's third goal was down to poor defending from the hosts. Lillis failed to cut out Craig Woodman's cross from the left and O'Flynn had the simple task of running the ball into an empty net.
Terry Gornell pulled one back for the hosts in the 67th minute and headed home Andrew Tutte's cross in time added on, but was then sent off for kicking out at former Dale defender Kevin Amankwaah as the attempted comeback fell short again.
Graham Alexander's first game in charge of Fleetwood ended in a goalless draw with Southend on Saturday afternoon.
Substitute Darryl Duffy grabbed the winner ten minutes from time as Cheltenham came from 2-0 down to beat Northampton 3-2 on Saturday.
Top-scorer Adebayo Akinfenwa gave Northampton a second-minute lead with his 14th goal of the campaign, firing home from just inside the box after Emyr Huws set him up.
The hosts doubled their advantage in the 14th minute when Robins defender Billy Jones could only manage to put the ball past goalkeeper Scott Brown.
But the Robins shot-stopper kept his side in the game, foiling Lewis Hornby, Ishmel Demontagnac and Keith Lowe as Northampton looked for a third goal.
Cheltenham got back on level terms with two goals in three minutes.
Darren Carter reduced the arrears in the 25th minute after Chris Zebroski did well to pull the ball back for the midfielder to net from close range. And Zebroski equalised two minutes later when he headed home a cross from Jones.
Former Cobblers striker Shaun Harrad went close just after the restart but Brown thwarted Akinfenwa who also headed wide. And it was Cheltenham who won it in the 80th minute when Duffy scored after being picked out by Carter's pass.
Stacy Long's deflected goal was enough to rescue AFC Wimbledon a 1-1 draw at fellow strugglers Barnet on Saturday afternoon.
The Dons looked to be heading for a fourth straight defeat in all competitions after Jake Hyde headed the home side in front after 64 minutes.
Luke Moore wasted a great chance to level with 15 minutes to go but Long's strike from outside the box deflected past goalkeeper Graham Stack in the 84th minute to earn Neal Ardley's side a point.
Bradford warmed up for their Capital One Cup quarter-final against Arsenal with an Alan Connell-inspired victory over Torquay which lifts the Bantams above Rotherham into fourth. Connell grabbed the only goal five minutes from time against his former club.
Bristol Rovers dropped in to the bottom two with a 1-0 home defeat to Dagenham and Redbridge, who won the match courtesy of Sam Williams' seventh of season.
A Jamal Fyfield own goal and Nick Chadwick's 90th-minute strike gave Plymouth a 2-0 win over York at Home Park.