In a scrappy opening, the visitors’ 3-4-3 formation frustrated Rovers early on, as it took the home side half-an-hour to seriously threaten Conor Winn’s goal, Shaw hooking over the top after they finally worked Simon Madden free down the right flank to cross. Minutes later Miele registered Hoops’ first shot on target before they took the lead on 36 minutes. Luke Byrne whipped over a superb cross from the left with Trevor Clarke getting a touch to pop the ball up for Shaw who volleyed home on the turn.
Gary Shanahan spurned a chance to level for Galway on 42 minutes.
Rovers upped the tempo after the break with the influential Graham Burke curling a powerful drive wide seconds after the restart before his cross on 57 minutes was headed over by Shaw.
Clarke then scampered through onto keeper Tomer Chencinski’s long clearance to bring a diving save from Winn. Well on top now, Shaw blasted wide from Miele’s cross on 66 minutes as Rovers pressed for a second goal.
That duly arrived two minutes later. Burke found Miele who held off a defender to smash a fierce shot to the net.
Chencinski was finally troubled on 73 minutes when tipping over Kevin Devaney’s shot from distance. But Rovers finished the stronger.
Chencinski; Madden, Devine (Bone, h-t), Webster (Meenan, 78), Byrne; McAllister; Clarke, Burke, Finn (Connolly, 72), Miele; Shaw.
Winn; Sinnott (Devers, 78), Grace, Folan; Shanahan, Holohan (Conway, 87), Byrne, Horgan; Melody (Kinneen, 90), Cunningham,Devaney.
Derek Tomney (Dublin).