There were also wins for Preston, Barnsley and Swindon while Crewe's miserable start continued with another defeat
Kyle Vassell struck his fourth goal in as many league games as Peterborough United won 1-0 at Bradford City in League One on Saturday.
Darren Ferguson's side bounced back from their midweek defeat to Sheffield United to move within a point of early leaders Fleetwood Town, with the 21-year-old striker netting the only goal of the game at Valley Parade.
Vassell got on the end of a pass from Michael Smith to settle a tight encounter, further enhancing his growing reputation.
Newly promoted Fleetwood kept a third successive clean sheet to continue their flying start to life in the third tier but they were unable to find a way past Chesterfield as they dropped points for the first time this campaign.
Preston North End remain within touching distance of the leaders thanks to Jack King's fourth-minute strike against Oldham Athletic.
The midfielder scored early on at Deepdale to seal a 1-0 win as Preston climbed to third on goal difference ahead of Bristol City, who were denied a win as Ian Henderson's 56th-minute leveller grabbed Rochdale a 1-1 draw at Spotland following Luke Freeman's opener.
Barnsley and Swindon Town complete the top six after both sides enjoyed comfortable home wins over Gillingham and Crewe Alexandra respectively.
Danny Wilson's Barnsley side have put their opening-day defeat to Crawley Town firmly behind them and are unbeaten in the league since then, with Saturday's 4-1 win their biggest so far.
Dale Jennings - sent off in Barnsley's first game - made amends with the fourth goal at Oakwell after Conor Hourihane, Sam Winnall and Devante Cole had put the hosts in a commanding position.
Crewe's miserable start continued as goals from Yaser Kasim and Andrew Williams gave Swindon all three points, leaving Steve Davis' side the only team without a point after four matches.
Kyle Bennett's second goal of the season was enough to give Doncaster Rovers a 1-0 win over Colchester United, while Sheffield United recorded the same scoreline against Crawley.
Notts County went one better as they beat Port Vale 2-0 to become the first side to stop Vale scoring this season.
Meanwhile, Leyton Orient's hangover from their play-off final defeat last season continues as they were held to a goalless draw by Walsall.
There was also a goalless draw between MK Dons and Coventry City, while Scunthorpe United's 1-1 draw with Yeovil Town gave the former their first point.