The under-21s beat Spurs 3-1 at the Tottenham Hotspur Stadium in the PL2 title play-off semi-finals.
They will now play Manchester United, who beat Manchester City 4-3, in the final.
Shannon Ruth’s side impressed in North London to follow previous knockout wins over Ipswich, where they trailed, and West Ham, who they swept aside 3-0.
The play-offs were brought in to give young players experience of handling high-stakes fixtures at the end of the season and the young Seagulls have responded in style.
They went ahead on 29 minutes with a close-range finish by defender Noel Atom, who was up for a corner.
Amid a melee, Atom found the ball conveniently at his feet and thumped it high into the net.
Harry Howell hit the post before the break.
The second goal came 11 minutes after the break and was turned in by Shane Nti from a low cross by Miah Oriola, who had been found by a long ball from goalkeeper Steven Hall.
Spurs replied almost immediately with a penalty converted by Mason Melia.
But Albion restored their two-goal advantage on 79 minutes from another corner.
Atom and Callum Mackley both won headers before Kofi Shaw finished.
The date and venue of the final have yet to be announced.
Albion’s academy face Three Bridges in the Sussex Transport Senior Cup final on Wednesday.
Albion: Hall; Albarus, Barclay, Atom, Keogh; Middleton, Robertson (Mackley 64); Silsby (West 89), Howell, Oriola; Nti (Shaw 72). Subs not used: Jensen, Belmont.