After a goalless first half, Deane Smalley and James Constable put the visitors two goals ahead just after the hour mark.
Jordan Chappell halved the deficit for the hosts with 20 minutes to play, but Asa Hall then secured the three points for Chris Wilder's side.
Phil Brown's Southend are the only other side with a 100 per cent record in the division after their 2-0 victory over Northampton Town.
Elsewhere, a John O'Flynn double helped Exeter move into fourth as they beat AFC Wimbledon 2-0.
Jeff Hughes and Jamille Matt pulled two goals back for Fleetwood, but Gary Rowett's men kept their noses in front to move up to fifth in the table.
Ollie Palmer's 78th-minute strike secured Mansfield's first win of the new campaign, while Andy Sandell's penalty just before half-time gave Newport their second victory.
Bury's 3-0 win over Accrington left the visitors bottom of the table and gave Kevin Blackwell's side their first points of the season. Meanwhile, Portsmouth beat Morecambe by the same scoreline at Fratton Park, and Plymouth won 3-1 at Cheltenham.
Rochdale and Chesterfield shared four goals in a 2-2 draw, while Dagenham and Redbridge scored an injury time equaliser to cancel out David Mirfin's 88th-minute strike for Scunthorpe.
The only game in League Two without a goal came at Bootham Crescent as York and Hartlepool battled for a point - Hartlepool's first of the campaign.
