Drogheda, with seven ex-Monaghan United players, including six from last year’s promotion winning side, continued their winning form that sees them riding high in third place in the Premier Division.
Declan O’Brien broke the deadlock in the 43rd minute when he capitalised on some indecision in the home defence and slotted the ball into the net.
As half-time approached, another former Monaghan United player, Ryan Brennan, was given his marching orders for an over the top tackle on Monaghan captain Robert Bayly.
Despite having the numerical advantage in the second half, and having most of the ball, Monaghan United were unable to find an equaliser.
MONAGHAN UNITED: C Bennion; P Whelan, A Byrne (R Collins 39), S Maher, A Collins (W McDonagh 27); G O’Connor, R Bayly, J Keegan; C Murphy, O Humphrey (D McGuinness 50).
DROGHEDA UNITED: G Sava; S Quigley, D Prendergast, A McNally, S Grimes; B Gannon, E Foley, G Brennan, R Brennan; S Brennan (J Breen 66), D O’Brien (P Hand 57).
Referee: Neil Doyle.