Johnson posted a three-under 68 despite bogeying two of his last three holes at Hilton Head, with Poulter and Lowry a shot back on nine under alongside Rory Sabbatini.
Patrick Cantlay and Scott Piercy are part of a group of six players sitting two strokes off the pace, with 19 players heading into the final round within four shots of the lead.
“I think I have been driving it well,” Johnson said. “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.”
Lowry had held the overnight lead despite being one of a number of players who had not finished their second round before bad weather struck in South Carolina on Friday.
After finishing on Saturday morning with a three-under 68, Lowry followed birdies at the par-five second and fifth by holing a 30-footer at the par-four ninth to extend his advantage.
The Irishman failed to get up and down from the greenside bunker to save par at the 13th and dropped another shot after finding water off the next tee, before bogeying the 16th to drop off the top of the leaderboard.
Johnson made his move with three consecutive birdies from the 13th, including a 45-footer on the 14th, only to post back-to-back bogeys from the 16th.
Poulter recovered from firing his opening tee shot out of bounds and making a double-bogey to card six birdies and post a four-under 67, with Sabbatini also one off the lead after a 68.
Eddie Pepperell is five strokes back in tied-20th after a 68, with Luke Donald and Tommy Fleetwood a further shot behind on four under.