Both sides fielded six new players and Walsall's promising start was rewarded when Whing headed a deep Rhys Weston cross into his own net in the 30th minute under pressure from Troy Deeney.
Brighton improved after the break and came closest to equalising when substitute Nicky Forster put a glancing header just over.
Former Derby striker Liam Dickinson sparkled at times for the Seagulls but Walsall held out after defending for long periods in the second half.
Brighton began the second half with more urgency and Mark Wright, fed by Forster, had a low shot saved by keeper Clayton Ince.
The Seagulls almost levelled after 62 minutes when Dickinson turned and fed Forster whose glancing header flew inches over the bar. Dickinson was narrowly off target with a ferocious drive from long range before keeper Ince dived to save his low goalbound shot.