Goals in each half from Christian Nanetti and Sahr Kabba handed the Hawks a thrilling 2-1 FA Trophy win at Sutton United.
Nanetti scored with a first-half penalty – and missed another before the break – before Kabba sealed the win eight minutes from time.
Craig Dundas pulled a goal back with five minutes left on the clock but it proved too little too late for the hosts.
Tom Dunford’s double and Justin Bennett’s hard-earned goal also secured Gosport Borough’s place in the first round proper of the FA Trophy after a convincing 3-0 win over Dorchester.
Elsewhere AFC Portchester’s fine second-half turnaround earned a 3-1 win over Western League side Shepton Mallet, and a place in the last 64 of the FA Vase.
The hosts trailed at the break to Robbie Maggs’ opportunistic strike but Jack Salter-Vaile, Danny Thompson and Simon Woods turned the tie on it’s head after being sent out early for the second half by manager Graham Rix.
But Fareham Town crashed out of the FA Vase after losing 3-0 to Western League side Bitton in their tie at Cams Alders.
Luke Bryan’s double and a Dan Spill strike sent the Wessex League premier division side packing.
Meanwhile, in the Wessex League premier division, Horndean recorded a hard-fought 2-1 victory at Fawley as Alex Miroy and Louis Brooks scored for the visitors.
Hayling United were left disappointed, though, after a last-gasp New Milton goal saw them drop two points in a 2-2 draw in Wessex League division one.
Darren Williamson had earlier put the Humbugs ahead before Scott Hamilton restored their one-goal advantage from the penalty spot.