Lowry's lead evaporated with three bogeys on the back nine and he finished with an even-par 71, tied for second on nine-under along with Ian Poulter (67) and Rory Sabbatini (68) at Hilton Head Island's Harbour Town Golf Links.
Six others were tied a shot further back on eight-under 205.
"I think I have been driving it well," Johnson told CBS television. "That's a big key around here.
"The wind direction was a lot different than it has been the last two days. The course played very difficult, especially the last three holes. It was hard to make putts."
But make putts he did, none bigger than a 47-footer at the par-three 14th.
"I don't know what to say about that one," said Johnson. "But it was nice."
That birdie got Johnson to within one of Lowry and when he picked up another stroke at the next the American had his nose in front.
Lowry, who started play shortly after sunrise to complete the final two holes of his second round, was cruising along with a three-stroke lead until the wheels fell off.
The 32-year-old dropped a shot on 13 after his tee shot found a bunker, then dropped another at the very next hole when his first shot went into the water.
He counted himself lucky to escape with a bogey four.
"I was trying to get out of there with a five. And holed out with a four and obviously that was huge," said Lowry, who went on to record his third bogey of the back nine on the 16th.
Still he was optimistic.
"It's nice only one behind," the Irishman said. "Even making those bogeys, it was the best I've been in a while."
Poulter got off to a horrible start but was faultless the rest of the way.
"I started with a double bogey, which is not very helpful," the Englishman said. "From that position on obviously I played some great golf. I holed a couple of nice putts and played real solid where I needed to."
Six birdies put him in contention.
"As often as I've done that this year, I haven't quite finished one off," Poulter said. "It would be nice to go out tomorrow and be aggressive where I can, and obviously see if I can go close."
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Peter Rutherford)
