The Slovenian showed his mettle to see off Loic Meillard in 1:28.80 to reign supreme in Austria and record his nation's first-ever giant slalom World Cup victory.
The 26-year-old sat in fourth place going into the second run but showed his guile on a tough track to top the podium by a healthy 0.19 secs margin.
French skier Matthieu Faivre claimed bronze to edge out Germany's Stefan Luitz by 0.08 secs.
Hirscher: It's amazing and surreal to set new Austrian record
Kranjec storms to Saalbach-Hinterglemm victory
Speaking after the race, Kranjec said: "In the past few years a lot of the younger guys came on the top or close to the top, it was just about time some new faces were on the podium."
Reigning Olympic champion Hirscher was vying for a fifth World Cup medal of the season and sits alongside Annemarie Moser-Proell as the joint third most successful skier on the World Cup circuit.
Zan Kranjec: I was on full attack mode, it paid off
But it wasn't to be on the day for the 29-year-old Austrian as he was denied back-to-back World Cup victories, finishing sixth in Saalbach.
Despite the result, Hirscher still tops the 2018/19 World Cup standings with 420 points as Kranjec moved up to seventh.
Matts Olsson crashes out in second run
'Monumental!' - Hirscher wins Saalbach-Hinterglemm slalom to set new record
Hirscher leads after dominant first run in Saalbach-Hinterglemm slalom