It was Hirscher's third win in four days after he also took the slalom in Zagreb on Thursday, keeping him on course for a seventh successive overall World Cup title.
Hirscher, who will be aiming to add a first Olympic gold in Pyeongchang next month to his glittering array of titles, has won seven World Cup races this season in all disciplines and took his career tally to 52.
Only 16 hundredths of a second separated Hirscher, Matt and Norway's Henrik Kristoffersen who finished third to continue his run of narrow misses.
Kristoffersen, runner-up in six races this season, was fourth fastest on the first run and looked as if he might claim a win as he took the lead with an overall time of one minute 51.10 seconds after his second.
But his hopes evaporated when Matt, starting last-but-one, sneaked inside his time by 0.03 seconds. Not to be outdone, Hirscher cut a further 0.13 seconds off Matt's time to maintain his winning routine.
Hirscher, who has 874 points in the overall World Cup standings, extended his lead over Kristoffersen to 154 points with Frenchman Alexis Pinturault a distant third on 547.
(Writing by Brian Homewood in Berne; Editing by Toby Davis)
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