Republic of Ireland, with the required winning margin no doubt in mind, made a bright start to the game with Zara Kramzar forced to make a crucial clearance off the line to block Noonan's header from an early corner.
Zala Mersnik was then called into action to thwart Abbie Larkin's shot from range after clever build-up play by the forward.
The home side broke the deadlock in the 19th minute when Noonan nodded Stapleton's looping delivery over Mersnik.
Republic of Ireland pushed for a quick second with Katie McCabe's free-kick gathered by the busy Mersnik and Kyra Carusa heading narrowly wide.
Stopper Mersnik then made another save to thwart Emily Murphy's chance and to deny the forward a second goal in two games after her late winner in Turkey last week.
The hosts were nearly made to pay for not taking advantage of more of their chances with Courtney Brosnan forced to make a diving save to stop Lara Prasnikar's shot just before the break.