In one minute and 56.17 seconds, the Austrian also snatched his third win of the season and his second in succession in the discipline.
It was also his ninth back-to-back podium in technical events, a consistency seldom seen since Alberto Tomba in 1991-92.
"It makes me twice as glad to know I'm the first to achieve a double here," said Hirscher, simply stunning in the afternoon's second run.
Slalom World Cup holder Andre Myhrer had set the bar very high in the fog and on the rutted terrain of the piste.
Hirscher's father Ferdinand was slightly worried when his son took off though the Austrian was not.
"I simply did what my father always told me to do -- no pressure, only pleasure. It might have looked like I was dancing between the poles, but I'm an excellent dancer," said Hirscher.
Sweden's Myrher had to be content with second, 0.57 adrift while Austrian Mario Matt, another former winner on the Sjeme hill, came third over a minute off the pace for his first podium of the winter, the 35th in his career.
Hirscher's second top spot in a row in the Croatian capital could be, like a year ago, a turning point in the season since Hirscher now leads Norway's Aksel Lund Svindal by 51 points in the race for the big globe.
Hirscher could still increase his lead in the classic Adelboden weekend a week away with a giant slalom and a slalom on the programme, but he refused to look too far ahead and instead savoured his 15th World Cup victory.
"It would be significant if this was March 25. But we're only halfway through the season and this is not the time or place to talk about the World Cup yet," he said.
Local favourite Ivica Kostelic, who has taken part in all six editions of the Zagreb slalom and made it to the podium four times, had to be content with eighth, his ailing right knee proving too much of a restriction on the bumpy course.
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