But the Scots looked shaky during an error-strewn first half and Titi Lamositele's 21-minute try allowed the USA to claim a 13-6 half-time lead.
However, a score 90 seconds into the second period from Tim Visser settled the Scots and they ran in four more scores from Sean Maitland, WP Nel, Matt Scott and Duncan Weir to claim the extra point.
The Scots now top Pool B with 10 points, three ahead of the Springboks - who they face on Saturday in Newcastle.
Their joy was slightly tempered, however, by the sight of stand-off Finn Russell going off midway through the second half with an ankle injury.