Vale started the day in second place but Gillingham seized the initiative when Burton netted with a close-range header, before Chris Whelpdale's 25th minute drive from the edge of the box rounded off the scoring.
And the day got better for Gills as third-placed Exeter suffered a 2-1 defeat at Southend which leaves the Kent side with a six-point lead at the top of the table after just eight games.
Scot Bennett's 51st-minute opener looked set to maintain the Grecians' good start to the season but Barry Corr equalised on 78 for the Shrimpers and Freddy Eastwood headed an 88th-minute winner.
Bradford's promising start continued as they won 2-0 at Oxford. After a goalless first half, Andrew Davies opened the scoring after 52 minutes and Nakhi Wells made sure of the points midway through the second half.
New boys Fleetwood, who started the day in fourth, were held to a goalless draw at struggling Bristol Rovers, while rock-bottom Barnet also drew 0-0 with Rotherham, who had Alex Revell sent off 10 minutes from time.
A late penalty double from Warren Feeney helped Plymouth strike back from 2-0 down and claim a 3-2 win at Morecambe.
Jack Redshaw and Richard Brodie had put the home side in command before Ross Jenkins narrowed the deficit on 72 and Feeney kept his nerve from the spot twice in the last 10 minutes.
Dagenham & Redbridge are still searching for their first win but will be happy to come away from Spotland with a 2-2 draw.
Rochdale led 2-0 at the break through Dele Adebola and Bobby Grant but the game changed when Kevin McIntyre was sent off on the hour. Michael Spillane scored from the resulting penalty, and Sam Williams hit the equaliser on 68.
Padraig Armond clinched the points with an 89th minute winner for Accrington at home to Aldershot, who had Peter Vincenti sent off for violent conduct in injury-time.
Calvin Zola's 89th minute goal earned Burton a draw at Torquay, who led through Rene Howe's 18th-minute goal.
Sammy Moore's 40th minute effort gave AFC Wimbledon a 1-0 win at Wycombe, while the games between Northampton and Chesterfield, and York and Cheltenham ended goalless.