Saadi embarked on a scintillating 50-yard run before firing past former Poppies goalkeeper Max Frampton to cancel out Joe Sanger’s opener for the Harlequins.
But his memorable 14th-minute effort proved academic as goals either side of half-time from Jack Slade and Graham Mankin restored the visitors’ lead.
And although Martin Warren struck to reduce the arrears midway through the second half, Poppies were unable to fashion another equaliser as Bemerton completed a league double.
Meanwhile, Christchurch were on the receiving end of a Warren Bentley four-timer as Alresford sentenced them to their heaviest league defeat for four-and-a-half years.
Bentley led the way as the Magpies registered a 7-1 victory at Arlebury Park with Zach Glasspool, Michael McEnery and Stuart Mott also on target.
Priory, who replied through Mark Smith’s penalty, beat Alresford 6-0 at Hurn Bridge in April 2010 with the Hampshire outfit getting their revenge as Christchurch suffered their worst defeat since Poppies put seven past them without reply in August 2009.
Poppies: Vaughan, Martinez, Jackson, Costello, Owens, Richardson, Ingram (Rowley, 22), Ward, Warren, Robinson (Pekun, 66), Saadi. Unused subs: Turner, Pearce.
Priory: Field, Cullen, Doe, Donachy, Baker, Blackburn, Smith, Fairbrother (Carter, 55), Saul (Landers, 80), Head (Proudley, 65), Hanratty.