The South African referee Craig Joubert was wrong to award a 78th-minute penalty against Scotland in their World Cup quarter-final loss to Australia at Twickenham, says World Rugby.
Scotland led 34-32 when Joubert ruled Jon Welsh was deliberately offside for playing the ball following a knock-on by a team-mate.
The governing body said that, because Australia's Nick Phipps touched the ball, "the appropriate decision should have been a scrum to Australia for the original knock-on".
Scotland lost 35-34 after Bernard Foley kicked the penalty.
A World Rugby statement read: "The match official selection committee confirms that Joubert applied World Rugby law 11.7 penalising Scotland's Jon Welsh, who had played the ball following a knock-on by a team-mate, resulting in an offside.
"On review of all available angles, it is clear that after the knock-on, the ball was touched by Australia's Nick Phipps and law 11.3(c) states that a player can be put onside by an opponent who intentionally plays the ball."
The statement added that Joubert "could not refer to the television match official in this case, and therefore had to rely on what he saw in real time".
"Despite this experience, Craig has been and remains a world-class referee and an important member of our team," World Rugby high performance match official manager Joel Jutge said.