Tranmere Rovers have begun life in the National League with a 1-0 victory over Woking.
The Merseyside outfit suffered relegation from League Two last season, but a goal from Jay Harris earned them all three points at Prenton Park on Saturday afternoon.
However, Cheltenham Town, who also dropped out of the Football League in April, could only draw 1-1 at Lincoln City.
Eastleigh top the standings after the first weekend after they stormed to a 4-0 triumph at Southport, who had Andrai Jones sent off early in the second half.
Last season's playoff runners-up Grimsby Town have started the new campaign with a 2-2 draw away at Kidderminster Harriers after Aman Verma struck late on to deny the Mariners all three points.
Three of the newly-promoted sides won on Saturday afternoon, with Barrow coming from behind to defeat Dover Athletic 2-1, Boreham Wood finishing strongly to beat Halifax Town and Bromley recording an impressive win over Wrexham.
However, fellow newcomers Guiseley succumbed to a narrow loss away at Welling United, who secured victory thanks to a goal from Sahr Kabba.
Forest Green Rovers, who reached the playoffs last season, beat Altrincham by a 1-0 scoreline, while Ryan Bowman scored twice in the final 13 minutes to earn Gateshead all three points at Aldershot Town.
Chester FC and Torquay United also began the season with a win after they overcame Braintree Town and Macclesfield Town respectively.
Results in full: Aldershot Town 1-2 Gateshead, Altrincham 0-1 Forest Green Rovers, Barrow 2-1 Dover Athletic, Boreham Wood 3-1 Halifax Town, Bromley 3-1 Wrexham, Chester FC 1-0 Braintree Town, Kidderminster Harriers 2-2 Grimsby Town, Lincoln City 1-1 Cheltenham Town, Southport 0-4 Eastleigh, Torquay United 1-0 Macclesfield Town, Tranmere Rovers 1-0 Woking, Welling United 1-0 Guiseley
