Justin Thomas, who began the day four shots off the lead, fired a five-under par 65 final round to thwart Brooks Koepka's repeat bid and take the title at TPC Southwind.
Collin Morikawa, who had been the pacesetter through the first two rounds, rallied from three strokes down with three holes remaining to force the playoff at Muirfield Village Golf Club.
Golf returned to the Olympics in 2016 after a 112-year absence but Tiger Woods, who dominated the sport in the first decade of the 21st century, missed its return through injury.
A statement from the PGA Tour said four fans were injured after two lightning strikes hit trees near the 16th tee at East Lake Golf Club in Atlanta, showering debris over nearby fans.
Shubhankar Sharma closed with a three-over 74 that included five bogeys and just two birdies and left him tied for ninth, six shots adrift.