The 19-year-old won the women's 10m air rifle title at the Deodoro shooting venue, holding her nerve to see off China's Du Li on the final shot.
She finished with 208 points, one clear of 2004 Athens champion Du. Bronze medal went to China's defending champion Yi Siling.
Olympic chief Thomas Bach looked on in the crowd as the first of 12 gold medals in play on a crammed opening day was awarded. There are more than 300 titles on offer over the next fortnight at the 2016 Olympics.
An absorbing competition was led briefly by Daria Vdovina, one of the Russian contingent competing in Rio in the shadow of the massive doping scandal that has dogged the Games build-up.
She eventually slipped off the pace to finish fifth.
Yi was bang in contention to successfully defend her 2012 crown but sharp shooting saw Thrasher and Du go head to head, with the American, displaying maturity beyond her years, edging it on the final shot.
For New York native Thrasher this was a dream Olympic debut after only taking up the sport four years ago.
