Tarpey was then denied by Valerie Pajetat at his near post, as the in-form striker looked into the mood to add to his 43 goals this season.
The deadlock was broken soon after though, as Harry Pritchard lined up a free-kick, curling it low past the wall and into the bottom corner.
Alan Massey headed over the bar from a Pritchard cross, while Tarpey flew down the left only to be denied by Ben Swift’s clearance as the visitors dominated.
However, Margate had a couple of chances on the break as Swift nodded just wide of the target and Jack Evans chipped a shot over the bar from 25 yards.
Tarpey came agonisingly close to extending his team’s lead early in the second half, as he lifted the ball over Pajetat, only to see Swift make a superb goal-line clearance.
However, he wasn’t to be denied a minute later when his well struck shot was deflected home.
Just before the hour, Maidenhead effectively sealed their place in the top tier of non-league football as Pritchard found the net for the second time, with another deflection deceiving Pajetat.
Tarpey somehow fired wide with the goal gaping late on, but it wasn’t to matter for Maidenhead as they eased their way to promotion, condemning Margate to the foot of the National League South table.
Margate: Pajetat, Seesegnon, Palmer, Hamilton, Foster (Brown 86), Swift, Evans, Rogers, Akindayini, Ngamvoulou (McFarlane 81), Martin. Subs not used: Miles, Fanimo.