Open organisers the Royal & Ancient said in a news conference that world number 44 Matsuyama was punished for slow play at the par-five 17th hole.
Laird, who is ranked 49th, was penalised for touching the ball with his hand at the same hole.
"He hit a second shot in the rough and ... marked the position of the ball and touched it and just moved it ever so slightly," said David Rickman, the R&A's executive director for rules and equipment standards.
"This is a situation covered by Rule 12-2 which requires the player to announce to his fellow competitor, before getting his hand on the ball, either to move it slightly or to lift it ... and he didn't do that."
The Scot had to sign for a seven at the 17th and wound up with a ugly 81 for 222, nine over.
Matsuyama and American Johnson Wagner were initially put on the clock on the 15th hole as they were 15 minutes over the scheduled time and out of position on the group ahead.
The Japanese's first 'bad time' was recorded at one minute 12 seconds on his first putt on the 15th.
Matsuyama transgressed again at the 17th and, as a result, his par-five turned into a six.
He went on to bogey the last to finish with a one-over 72 and a three-over total of 216.
(Editing by Ed Osmond and Sonia Oxley)
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