Reigning gold medallists Fiji rallied in the second half to defeat Japan 24-19 in a rematch of the Rio 2016 semi-finals.
Fiji trailed 19-12 but fought back through a pair of tries and a conversion from substitute Waisea Nacuqu in the final four minutes.
The team they beat for gold five years ago, Great Britain, opened play with a flourish, thrashing Canada 24-0, while New Zealand crushed South Korea 50-5.
Fourth-place finishers in 2016, South Africa defeated Ireland 33-14 while Argentina beat Australia 29-19 and the United States edged Kenya 19-14.