Scotland head coach Pedro Martinez Losa’s claim that there was “no way” his side were going to lose in Edinburgh had raised a few eyebrows considering the rather laboured 1-0 first-leg win.
Opposition team boss Alexandra Szarvas responded by stating she was “100% confident that we can be successful”.
That was equally bold considering her side had never beaten the Scots in four meetings, sit 23 places below their hosts in the world rankings and had only finished third in their qualifying group.
It seemed like a shock could, nevertheless, be on the cards when Martinez Losa’s side looked leggy and nervous as they survived a couple of early Hungarian surges into their penalty box.
However, after Lisa Evans found Sam Kerr with a neat cutback from the byeline and the midfielder’s 15-yard drive came off the underside of the bar, off the heel of the goalkeeper and over the line, all doubts were suddenly extinguished.
Cuthbert’s thundering second from just outside the penalty box will be added to the midfielder’s Scotland tally despite a nick off a defender helping it loop over Brzykcy – and the tie was over just after the half-hour mark.
Fellow midfielder Weir celebrated her second Scotland appearance since her year out through injury by pouncing on a clever Thomas backheel before the striker slotted one of her own.
A final play-off secured with a seventh win a row, four at home, and an eight-game unbeaten run, but Scotland now face a much tougher task against the last side to beat them – Finland winning on penalties at the Pinatar Cup in February.
Marko Saloranta’s side are three places below the Scots in the world rankings, but they also showed their quality earlier in the day with a 5-0 demolition of Montenegro to secure their progress 6-0 on aggregate.
However, on the eve of Halloween, while they know improvement is still needed, the Scots will be dreaming of extinguishing the ghosts of their 1-0 Euro 2021 qualifying defeat by the Finns at the same venue when they return for the first leg next month.