Holdener was down in seventh after the opening downhill with a deficit of 0.94sec, but showed all her slalom prowess to time a combined 1min 58.88sec.
Her Swiss teammate Michelle Gisin claimed silver at a razor thin deficit of 0.05sec, with Austrian Michaela Kirchgasser taking bronze (+0.38).
Holdener's vaunted teammate Gut was earlier ruled out of the competition after crashing during the warm-up for the slalom and injuring her knee.
Gut had finished third in the downhill, but was evacuated from the Corviglia slope by helicopter after her fall.
"Lara fell while warming up for the slalom," a Swiss team spokesman told AFP. "She was taken to hospital in St. Moritz for tests."
Swiss women's coach Hans Flatscher told Swiss television: "It's very bad. Her knee is not at all good."
In Gut's absence, there was drama to the end for home fans as Holdener and Gisin awaited with baited breath the descents of Slovenia's Ilka Stuhec and Italian Sofia Goggia, leader after the downhill, having hit a top speed of 121kph down a course shortened because of heavy early morning snowfall.
With Swiss flags waving, Stuhec, winner of this season's sole combined event in Val d'Isere in December, lasted but three gates before sliding out.
Then came the turn of Goggia, the Italian suffering the same fate after six gates to allow the large partisan home support a large amount of succour after the loss of Gut.
There was heartbreak for Vonn, a three-time World Cup combined crystal globe winner, unable to make up the leaders' deficit despite a gutsy slalom run.
Vonn eventually finished fifth, 0.85sec off Holdener's pace, and will be left decrying what was in her books a mediocre sixth best downhill, albeit with her right hand taped to her pole to better help with gripping problems linked to the broken humerus she sustained in November.