Gavin Brennan scored before setting up Danny North for a second as Shamrock Rovers closed in on a Europa League spot.
A second victory in the week has Hoops just two points behind second-placed Cork City in the Premier Division table.
It also took Rovers eight points clear of St Pat's in the race for third.
Defeat sees Galway drop to 10th place. Should Sligo beat Bray tonight, Tommy Dunne's side would be in the relegation play-off spot.
Far from the dour win over Bray midweek, Rovers dominated from the off and should have been more than a goal to the good at the interval.
The pressure finally told in added time at the end of the half. Left-back David O'Connor got forward to cross low from the right.
Gavin Brennan's initial shot was touched onto the near post by Conor Winn, but the ball came straight back to Brennan who, despite being on the ground, managed to scoop the rebound home.
A defensive blunder brought Rovers second goal on 66 minutes as Brennan robbed Kilian Cantwell to run clean through on goal.
Instead of scoring himself, Brennan laid the ball off for North to tap home to celebrate the birth of his second child, Daisy, earlier in the week.
SHAMROCK ROVERS - Murphy; Madden, Kenna Blanchard, D O'Connor; R Brennan (Duff 80), Cregg; G. Brennan, Drennan, Miele (McPhail 80); North (McCaffrey 86).
GALWAY UNITED - Winn; Raftery, Oji, Cantwell, Horgan; Keegan, O'Leary, Sinnott, Shanahan (Melody 74); Barry (Saarelma 60); Curran (O'Connell 69).
REF - A Buttimer (Cork)