They followed up a 3-0 curtain-raising National League South success against Welling by scoring an injury-time winner at Hampton & Richmond.
Sub Alex Wall struck the late, late decider after Jerome Slew had missed a 77th minute penalty for the hosts with the score at 1-1.
Slew had earlier bagged a first-half equaliser after defender Manny Adebowale - on loan from Crawley - had opened the scoring at the Beaveree.
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It is the first time Hawks have started with six points out of six since their debut season in 1998/99. Back then, Billy Gilbert’s side followed up a 2-0 victory at Chelmsford with a 3-0 home success against Newport.
Strikers Jason Lovell and Steve Tate scored those five goals between them, but this season five different players have already netted
Hawks boss Paul Doswell confessed: ‘A draw would probably have been the fairest result.
‘It was an excellent game. I felt we controlled the first half and they probably had the second.
‘We dictated the tempo of the first half before giving them a leg up back into it with the equaliser.
‘The turning point was obviously the penalty miss.’
‘I wouldn’t say we were lucky - both teams competed well. I don’t think many sides will come here and win this season.’
Doswell was forced into two changes from the starting XI against Welling. Paul Rooney and Josh Passley picked up injuries two days earlier in training with Billy Clifford - a goalscoring sub against Welling - and Michael Green replacing them.
Centre halves Sam Magri and Jamie Collins remained injured, with Doswell only naming two outfield subs - Wall and Abdulai Baggie - plus keeper Charlie Searle.
Goalkeeper Ross Worner played despite a swollen ankle while midfielder Oscar Gobern only started after passing a late fitness test.
After the teams had traded first-half goals, Worner brought down David Fisher to concede a penalty 12 minutes from time.
But Slew fired his spot-kick well over the bar, with Hawks grabbing the victory late on when Wall reacted first after Jake McCarthy’s header from a corner had been saved by Alan Julian.
‘We know these things will go against you at times this season and it will be the worst feeling in the world,’ said Doswell.
‘As it is, we will travel back with the best feeling in the world.’
With no fixture next weekend, due to an odd number of teams in the NLS, Hawks will bid for a third straight win on Bank Holiday Monday at Chippenham Town.
They then travel again on September 4 to fellow promotion hopefuls Ebbsfleet United.
Hampton had started the season with a five-goal romp, at Eastbourne, and Ebbsfleet had done the same - caning Tonbridge Angels 5-1.
Fleet were inactive yesterday as Chippenham had called their scheduled game off for Covid reasons several days earlier.
Hawks are one of just two clubs that have six points out of six in the NL South.
Dartford are top on goal difference after a 3-0 win against Slough with goals from Ade Azeez, Noor Husin and George Porter.
Hawks: Worner, Newton, Oastler, McCarthy, Adebowale, Green, Clifford, Gobern, Roberts (Baggie, 66), Rendell (Wall, 70), Wright.