Goals from James Hayter and Ben Swallow fired the Hawks through in the FA Trophy as they beat Basingstoke Town 2-1 at Westleigh Park.
Hayter gave the Hawks an early lead, before the Dragons levelled with a penalty before half-time.
Swallow curled home the decisive strike 10 minutes from time.
Finalists from two seasons ago, Gosport Borough crashed to a surprise 2-1 defeat at Southern League Cirencester Town.
Two Charlie Griffin goals put the hosts in charge, with Borough only managing a Brett Poate goal before the break.
A stoppage-time penalty from Jason Prior took the Rocks through with a 1-0 win over Bath City at Nyewood Lane.
With a replay looking almost certain, Prior kept his composure to snatch the win.
In the Southern League central division one, Peterfield suffered late agony as they suffered a 1-0 home defeat to AFC Rushden & Diamonds at Love Lane.
AFC Portchester powered to a confident 3-0 win at Hamworthy United in the Wessex League premier division.
MeANWHILE, Moneyfields surprised highly-fancied hosts Blackfield & Langley with a 1-0 win at Gang Warily.