Bray had an early let-off when keeper Matt Gregg deliberately handled the ball outside his penalty area.
The resulting free by Gavin Brennan was touched round the post by Gregg.
The Seagulls might have broken the deadlock on 20 minutes when Danny O’Connor and Dean Zamra combined nicely to set up a chance for Conor Murphy only for the young striker to miscue his effort.
Drogheda should really have taken the lead on 26 minutes when a misdirected back header from Dane Massey put Corcoran in the clear, but his hooked shot from the edge of the box was over the bar.
But the visitors took the lead one minute before the interval when Corcoran headed home from close range after good work between Lynch and Tiernan Mulvenna.
Drogheda might have stretched their lead on 57 minutes when the lively Mulvenna again shot inches wide after defender Stephen Quigley had created an opening on the right.
But Hand did double Drogheda’s lead on 81 minutes when firing home from 12 yards.
Substitute Dan McGunness did pull a goal back for Bray in the 89th minute when stabbing home a shot from close range after a Zambra cross — but by then it was too little, too late.
BRAY WANDERERS: Gregg; Doyle (G Kelly 68), Mitchell, Massey, Houston; Zambra, Dempsey, D.O’Connor, J Kelly; Murphy (McGuinness 62), Mulroy (Tresson 86).
DROGHEDA UTD: Trimble; Quigley, McNally, Rogers, Hand; O’Brien, McMahon, Lynch, G.Brennan; Mulvenna (White 86), Corcoran.
Referee: Rob Rogers (Dublin).