Robinson had stunned the Alpine skiing world by winning the season opener in Solden in Austria in October, in doing so becoming only the second Kiwi to ever win a World Cup race.
Defending champion and World Cup points leader American Mikaela Shiffrin was strangely off the pace, clocking the 19th fastest time in her opening run and finishing 17th overall.
Earlier Robinson laid down a solid marker in the first run with the seventh quickest time, clocking 1:07.64 seconds, just .49 of a second slower than Holtmann.
Robinson drops one place to sixth in the overall Giant Slalom standings, three points behind French star Tessa Worley. Brignone's win takes her to the top of the standings after three races.
Of the 66 starters the fastest 30 qualified for the second run which was held in reverse order. Robinson was seventh last to go.
Fellow Kiwi Piera Hudson had a disappointing day clocking 1:10.61 to finish 54th and not among the top 30 to earn a second run.
The next round of the World Cup is on December 28 in Lienz in Austria.