Alan Murphy had come close twice from distance for Galway before the Mons took a 13th minute lead, Sean Brennan full of trickery in the box before setting up Michael Isichei for a close-range finish.
Sean Brennan was guilty of a glaring miss, shooting wide with the goal at his mercy, as the more fluent home side sought to hammer home their advantage.
A blistering 33rd minute free-kick from Murphy that grazed the post gave the Premier side hope but just before the interval the Mons menace manifested again, Fabio O’Brien’s header from Paul Whelan’s cross flashing just wide.
Intense Mons pressure saw Sibanda clear off the line and then home captain Alan Byrne crash a shot off the crossbar. In the 77th minute, Galway almost snatched an equaliser, Ronan Cauldwell with a great effort from 20 yards that Gabriel Sava kept out with a flying save. A flare-up with 10 minutes left saw both Mons’ Eric Foley and Galway’s Sean Gavin sent off.
With three minutes to play Sean Brennan stole into the box and coolly converted Jordan Keegan’s cross to put Monaghan in command of the tie.
MONAGHAN UNITED: Sava; Whelan, A Collins, A Byrne, Grimes; Isichei (P Byrne 64 (McDonagh 85), Foley, R Brennan, Keegan (Marks 88); S Brennan, O’Brien.
GALWAY UNITED: Winn; Sinnott, Som, Gaughan, Kelly; Kim (Gavin 46), Ryan, Murphy, Sibanda (Silvera 76); Cauldwell, (Walsh 89) Gilmour.
Referee: D Tomney.