The controversy revolved around whether Johnson should have been penalised when his ball moved on the fifth green.
After speaking with Johnson on the 12th tee, officials informed other players a decision would be made post-round.
A penalty stroke was added to Johnson's score but he won by three from Lowry, who had three bogeys from the 14th.
American Jim Furyk shot a four-under 66 to finish tied for second with compatriot Scott Piercy (69) and Lowry.
England's Lee Westwood, playing alongside Johnson, started the day on two under par but had a 10-over 80 to finish on eight over.
The United States Golf Association (USGA) later said they wanted Johnson to know of the potential one-shot penalty so he could play accordingly.
However, it led to confusion for players and fans alike, particularly when Lowry birdied the 12th to get to four under and nobody knew for sure whether he was level with, or one behind Johnson.
Northern Ireland's Rory McIlroy, who missed the cut, said on Twitter while the round was in progress that no penalty was warranted and called the USGA "amateur", adding that he "wouldn't hit another shot until the farce was rectified", while world number two Jordan Spieth called it "a joke".
