Burton left Rotherham under a cloud seven years ago after handing in a transfer request and it was no surprise therefore that he was booed when he took to the pitch.
The former Derby striker had the last laugh, though, as his eighth and ninth goals of the season gave the visitors the win, with Jason Taylor on the mark for the hosts.
Second-placed Port Vale are now six points behind the Gills after their five-match unbeaten run came to an end with a 2-0 home defeat to Chesterfield.
Jay O'Shea and Tendayi Darikwa were on target for the Spireites, who moved up to ninth.
Cheltenham now trail Vale by just one point after Darryl Duffy's winner gave them a 3-2 victory over Northampton at Sixfields Stadium.
Adebayo Akinfenwa continued his fine form by giving Northampton the lead after two minutes and a Billy Jones own goal doubled the hosts' advantage.
Darren Carter and Chris Zebroski scored twice within the space of three minutes to make it 2-2, however, and Duffy sealed the win 10 minutes from time with a close-range finish.
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.
Fleetwood began life under Graham Alexander with a 0-0 home draw against Southend while bottom side Barnet drew 1-1 with AFC Wimbledon at Underhill.
Adam Mekki's late equaliser at Oxford was enough to move Aldershot out of the drop zone while Wycombe drew 2-2 with Morecambe at Adams Park.
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.
Rochdale's Terry Gornell scored a second-half double, but it was not enough to stop Exeter from moving into the play-off positions as they ran out 3-2 winners at Spotland.
A Jamal Fyfield own goal and Nick Chadwick's 90th-minute strike gave Plymouth a 2-0 win over York at Home Park.