The American, who was already four-over-par for the day, badly overhit a putt on the 13th green which looked in danger of rolling off the putting surface.
Mickelson controversially prevented that from happening by running after the ball and hitting it while it was still moving.
Officials could have chosen to disqualify Mickelson but instead elected to penalise the five-time Major winner, who shot an 11-over 81 to drop to 17-over.
The incident overshadowed the 66 from Daniel Berger which gave the chasing pack hope of catching leader Dustin Johnson at Shinnecock Hills.
US OPEN LEADERBOARD AFTER ROUND THREE
1. Daniel Berger (+3)
=. Tony Finau (+3)
=. Brooks Koepka (+3)
=. Dustin Johnson (+3)
5. Justin Rose (+4)