George Porter’s spectacular goal looked to have won it for the hosts, but Preston popped up to head in Ryan Sellers’s cross.
Josh Staunton made a welcome return from injury off the bench with an equaliser to cancel out Frankie Sutherland’s first-half opener.
Halifax could count themselves unfortunate to be behind when Sutherland smashed home the rebound after his penalty had been tipped onto the post by Sam Johnson.
From Simon Lenighan’s hopeful pass forward, Bromley needlessly conceded a corner, and from that, a floated cross from the right was met with a cushioned header by Staunton at the back post.
Sellers cleared off the line from Uzokwe, before Johnson spilled a header back across goal, requiring a scrambled clearance.
Bromley were in the ascendancy and their pressure told when Sutherland’s pass played in Porter, who produced a stunning volley across goal only for Preston’s late leveller to earn the Shaymen a point.
Bromley: Huxter, Okoye, Rooney, Holland, Wood (Taylor 46), Sutherland, Higgs, Porter, Luque (De Silva 90), Ogedi-Uzokwe, Bugiel (Myles-Meekums 31). Unused substitutes: Daniel Johnson.
FC Halifax Town: Johnson, Sellers, Clarke, Maher (Staunton 24), Hanson, Edwards, Lenighan, Berrett, Southwell (Wootton 71), Odelusi, Preston. Unused substitutes: Rowley, Duckworth, King.
Referee: S Purkiss (London).