Corsie nodded home to earn the Scots a 2-1 victory at Hampden and maintain their 100 per cent record in World Cup qualifying Group B.
Milan winger Christy Grimshaw had opened the scoring late in the first half but Scotland were punished for some slack passing when Fanni Vago levelled.
The visitors looked like holding out until Corsie came up with a thrilling finish.
Scotland had won 2-0 in Budapest last month but Spain scored seven there days later and Pedro Martinez Losa will know there is much improvement to be made before his side face his native country next month.
Jen Beattie had a decent early effort parried and Claire Emslie fired wide from 20 yards on the counter-attack but Scotland were slow to get going.
The hosts stepped up their pressure towards the half-hour mark and twice threatened following Caroline Weir corners. Beattie had a header well saved and centre-back partner Corsie saw her effort inadvertently blocked in the goalmouth by Grimshaw.
The latter netted herself in the 42nd minute when she took down Nicola Docherty's deep cross and dispatched the ball into the corner of the net.
Grimshaw drew an unorthodox save from the visiting goalkeeper just after the interval but Scotland were pegged back in the 56th minute.
The hosts did not look entirely comfortable playing the ball out from the back and Docherty was short with a pass back to a fellow defender. Hungary made the most of their chance with Vago finishing well after a swift exchange of passes.
Scotland looked shaken but they got going again and put on the pressure.
Emslie nutmegged a defender and curled inches wide, Beattie was denied by a last-ditch block and Corsie had a header saved.
The Scots were struggling to make the most of their corner count until Beattie won the second header following Erin Cuthbert's delivery and Corsie kept her nerve.
Scotland host Sweden in a friendly on Tuesday night before taking on Ukraine and Spain next month in their next two qualifiers.