Northern Ireland were given a huge left-off at the start of the second half as Krznaric found space in the area but Burns was alert to keep the midfielder’s effort out.
McKenna tried sparking the hosts into life as she worked her way into the box and her low, drilled effort was pushed away from Bacic.
Oxtoby introduced Louise McDaniel just shy of the hour mark, and McPartlan curled over from range but the hosts struggled to carve out any chances of note.
Izabela Lojna, who scored at both ends in the 1-1 draw in the first leg, skipped into the area and forced Burns into another strong save.
Magill, who has only just returned from injury for Birmingham City, was withdrawn with eight minutes to play and her replacement Emily Wilson immediately won a free-kick, with McPartlan heading wide.
Wilson was involved again after she was played through by McDaniel, but her pass across goal was cut out by Bacic.
There was a brief scare in stoppage time as Petra Pezelj fired straight at the keeper, but neither side could find the breakthrough and the game headed to extra time.
Extra time started with the same intensity that the second half ended with, and Maja Joscak had an effort deflected wide by McPartlan before the Croatian midfielder flicked her header over from the resulting corner.
There was a huge scare when Jana Canjevac fired across goal and Nat Johnson, introduced for her debut by Oxtoby, almost touched the ball over her own line but the 30-year-old was able to recover in what was the last play of the half.
After the restart, a combined heroic block by Rebecca Holloway and Johnson denied substitute Anela Lubina from 12 yards.
Having struggled to create any chances, Chloe McCarron found Lauren Wade on the edge of the area and her powerful effort was tipped over by Bacic with eight minutes to play.
But that was the moment that led to Wade’s stunning winner, as she reacted quickest to a ball on the edge of the area and her effort flew past Bacic to keep alive Northern Ireland’s hopes of reaching another tournament.