Haven topped Group A, and sealed a place in the final four, having scored just three goals more than Town.
Tuesday evening saw both Newhaven and Eastbourne Town run out 3-1 winners.
Haven saw off Little Common at home thanks to a brace from the prolific Lee Robinson.
The hosts lead 2-0 at half-time after Lukas Franzen-Jones and Robinson struck inside the first 15 minutes.
Robinson added his second of the night with 12 minutes to go before Nick Richardson struck a late consolation goal in added time.
Meanwhile Town triumphed in their trip to AFC Uckfield Town.
A cheeky dinked finish from George Cook gave the Uckers an unlikely half-time lead.
But Eastbourne Town rallied and goals from Harley Ransom, James Hull and Leke Ademola completed the turnaround.
Tuesday's results saw Newhaven finish top of the group with 15 points from six games, with Town just behind on the same number of points but three fewer goals.
Little Common finished third with four points, while AFC Uckfield Town propped up the group having taken a solitary point from their six fixtures.
Newhaven will travel to Group D winners Loxwood in the semi finals the week commencing Saturday, May 8.
Saturday saw Haven and Town pick up home victories. Newhaven beat AFC Uckfield Town 3-0 thanks to Ian Robinson's double.
Charlie Bennett and Robinson put Haven two goals to the good at the break before Robinson bagged his second, and Newhaven's third, in the second half.
Eastbourne Town overcame Little Common 2-0 at The Saffrons. Goals in each half from George Taggart and Leon Greig secured victory.