Josh Kerr drew Binfield into a smart close-range stop at the start of the second period when the central defender met Mandroiu's free-kick at the near post, and Tilley surged towards goal and forced the Pagham keeper into another save from a narrow angle.
A well-worked corner from the Seagulls then ended with Mandroiu rattling the crossbar, before Connolly's lob sailed over after the Irish forward had run in-behind the defence as Albion started the half in control.
But Mandroiu wasn't to be denied getting on the scoresheet, and he scored his sides third on fifty five minutes.
The influential midfielder picked up the ball on the edge of the area and stylishly worked himself some space before firing low and in off the far post past Binfield to all but end the game as a contest.
Gyokeres then replaced Jayden Onen on fifty nine minutes in Albion's first change, and the Seagulls would score their fourth of the evening soon after.
Moore's inviting cross from the right was headed back across goal by Connolly, and Davies was on hand to volley home to extend the lead.
Connolly then made way for Henrik Bjordal in Albion's final switch, and Davies would soon get his second and the Seagulls' fifth of the night with fifteen minutes left on the clock.
Cox marauded down the left wing once more and sent in another dangerous delivery, and the midfielder was on-hand to knock the ball home after Binfield had parried it into his path.
Two of the home side's substitutes then combined to make it six, as Bjordal twisted into space and floated the ball to the back post for Gyokeres to apply a simple finish.
The Swedish striker then rattled the crossbar having been played in by Bjordal as the visitors began to tire, and Rusk's men kept up their dominance until the end to reach the cup final.
(A selection of photographs can be found on Facebook - courtesy of Simon Roe Photography)
Stats: (Brighton & Hove Albion-Pagham)
Goals: 6-0; Shots: 18-13; Shots-on-target: 12-5, Fouls: 4-10; Offside: 5-0; Corners: 2-6; Yellow cards: 1-3; Red cards: 0-0.
Brighton & Hove Albion: Collings, Moore, Cox, Davies, Kerr, Dallison ©, Tilley, Mandrioui, Connolly, Cashman, Onen.
Substitutes: Gyokeres, Sanchez, O’Hara, Bjordal, Alzate.
Pagham: Binfield, Wiggins, Wollers, Davidson, Booker, Horncastle ©, Thurgar, Chick, Kasimu, Rowlett, Overton.
Substitutes: Van Driel, Bingham, Kilhams, Hawker, Parkinson.
Match report by Alex Stedman