Shiffrin was 1.36 seconds quicker than Italian Marta Bassino in second with Austrian Katharina Liensberger rounding out the podium.
Robinson showed blistering speed on the lower section of the course to improve her position and will be satisfied with the overall result, having never skied previously in Lienz.
Her coach Chris Knight was pleased with how she bounced back from a poor start.
"Yeah that was her normal skiing. She still had a mistake in her second run that cost her a few spots but overall a good performance. It's a really tough hill to turn up to having never skied it before," Knight old NZME.
After becoming the first New Zealander in more than two decades to win a World Cup ski race in the season opener in Solden in Austria, Robinson had a DNF - when short of preparation following a knee injury - in Killington in the US and then finished 10th earlier this month in Courchevel in France.
She remains 6th overall in the World Cup Giant Slalom standings while Shiffrin climbs two places to second behind Italian Federica Brignone, the winner of the last race in Courchevel.
However, Robinson is in the mix approaching the mid-point of the nine-race Giant Slalom calendar and is just ahead of reigning world champion, Slovakia's Petra Vlhova, who finished 5th in Lienz.
The next World Cup Giant Slalom is in Sestriere in Italy on the 18th of January.