Yeovil Town were quickest out of the blocks - Courtney Duffus' goal in the second minute giving them their first win of the season against Eastleigh.
Frustration for Wrexham. After taking a two-goal lead at Meadow Park, goals from Keiran Murtagh and Justin Shaibu saw Boreham Wood snatch their first point of the new campaign.
Solihull Moors netted three without reply against Torquay United.
A brace from Jamey Osborne, either side of a Terry Hawkridge penalty was enough for Tim Flowers' men.
Alfie Pavey's third goal of the season wasn't enough for Dover Athletic who slipped to a 2-1 reverse to Dagenham & Redbridge.
Barnet striker Simeon Akinola celebrated his birthday in style with a goal against Sutton United.
But the Bees could only scrape a point in South London.
Billy Bingham's 30-yard screamer was the pick of the goals as Bromley left Ebbsfleet without a win in their opening two games.
Halifax are the only team in the division with a 100% record.
Second-half goals from Josh Staunton and Tobi Sho-Silva edged them past Hartlepool United who are still looking for their first points.
AFC Fylde and Chorley played out a goalless draw at Mill Farm while Aldershot Town needed a first-half goal from Jacob Berkeley-Agyepong to defeat Woking.
Chesterfield are still searching for their first win but fought back late on to share the spoils with Maidenhead.
A goal in each half from Will Smith helped Harrogate Town on their way to a comprehensive 3-0 victory in Cumbria.
Connor Hall rounded things off against Barrow.
Notts County threw away their lead to draw with Stockport County.
Hatters midfielder Elliot Osborne's strike cancelled out Jim O'Brien's emphatic opener.
Tuesday's National League full-time scores:
AFC Fylde 0 - 0 Chorley
Barrow 0 - 3 Harrogate Town
Boreham Wood 2 - 2 Wrexham
Bromley 3 - 1 Ebbsfleet United
Dover 1 - 2 Dagenham & Redbridge
Halifax 2 - 0 Hartlepool United
Maidenhead 1 - 1 Chesterfield
Notts County 1 - 1 Stockport County
Solihull Moors 3 - 0 Torquay United
Sutton United 1 - 1 Barnet
Woking 0 - 1 Aldershot Town
Yeovil Town 1 - 0 Eastleigh