After a disappointing time-trial on Thursday, Armstrong was expected to fare better on the hilly 214km-stage from Dalton to Dahlonega that included five rated climbs.
Battling stomach cramps and driving thunderstorms, the Texan never looked like winning and eventually crossed the line in a small group, eight seconds behind the winner.
It was another disappointing result for Armstrong, who stamped his authority on six Tour de France victories with crushing performances in the mountains, fuelling more concern about his fitness ahead of this year's race.
Two of Armstrong's Discovery team mates made it across the line ahead of their leader, Russia's Viatcheslav Ekimov finished second and Jason McCartney fourth behind Saunier Duval rider Marco Pinotti of Italy.
It was a brave ride by Vandborg, who battled through the final stages without the assistance of any team mates.
"I was suffering quite a bit," Vandborg said.
"I think Eki (Ekimov) was closer to dropping me than he thinks he was, but it worked out perfectly."
"At the final corner, we were side-by-side and I just pushed the big gear. Luckily I succeeded."
American Floyd Landis, who snatched the leader's jersey with his victory in the time-trial, continued to top the overall classification 19 seconds clear of David Zabriskie.
Armstrong is 1:42 back in eighth, but with the one more day in the mountains to come, the Texan made it clear he would not be surrendering his title without a fight.
With four team members who will ride in the Tour de France, Armstrong's Discovery are certain to attack on the 182km-stage from Gainsville to Brasstown Bald, the highest peak in Georgia.
"Those Discovery guys have a strong team," Landis said. "It's going to be tough to beat them.
"They are going to gang up on us. I wouldn't say I'm the underdog. I'm certainly as strong as anyone in the race, but I'm outnumbered and that makes it difficult."