Aerni, 30th after the opening downhill leg, was first out of the start hut on the Suvretta slalom piste, with 2015 world champion Hirscher the third man down and finishing 0.01 of a second slower for silver.
Switzerland's Mauro Caviezel took the bronze, on a course set by a Swiss coach, with a combined time 0.06 slower than the winner.
The gold was host nation Switzerland's third in six races at the championships, with Aerni matching the women's combined gold won by Wendy Holdener on Friday. Beat Feuz took the men's downhill gold on Sunday.
Austria's Romed Baumann, a combined bronze medallist on home snow in Schladming in 2013, was fastest in the downhill but his 30th start position in the slalom worked against him on a softening slope and he finished 12th.
The top 30 skiers from the downhill started the slalom in reverse order with the medals decided on total times from the two disciplines.
(Writing by Alan Baldwin; Editing by Robin Pomeroy)
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