Hastings took the lead in the 16th minute thanks to a wonderstrike from Craig Stone, before former Worthing striker Ben Pope doubled The U’s lead two minutes into the second half.
The tie looked like it was coming to a close, but two goals in six minutes – a header from Lloyd Dawes and a rebounded tap in by substitute Ollie Pearce from Ricky Aguiar’s long range effort – levelled the match and took it into extra time.
With penalties looming, Jasper Pattenden was brought down around 30 yards out for a free kick.
Jesse Starkey floated the ball in, and was met by the head of Marvin Armstrong who nodded home from six yards out to send the Worthing faithful wild and The Mackerels into to second qualifying round.