US PGA champion Jimmy Walker held a two-shot overnight lead but shot a four-over 74 including two double bogeys.
Pieters birdied four of his first five holes before Johnson made a late surge and drew level on nine under par.
Northern Ireland's Rory McIlroy remains three shots back after a 68.
Scotland's Russell Knox is on five under, with England's Paul Casey four under. Open champion Jordan Spieth and England's Tommy Fleetwood are two under.
Pieters, a wildcard pick for Europe in last year's Ryder Cup, stormed into contention before stuttering on the back nine with consecutive bogeys on 13 and 14, eventually finishing with a 66.
After a mixed first nine holes, two-time major winner Johnson made birdies on 16 and 18 to card a 65.
Australia's Scott Hend is a shot behind on eight under after a superb 63, with world number three Hideki Matsuyama another stroke further back.
Meanwhile, Greg Owen has a five point lead going into the final round of the Barracuda Championship, which is the only PGA Tour event which uses the 'modified stableford' scoring system.
The format awards eight points for an albatross, five for an eagle and two for a birdie. A bogey results in a point being lost, while a double bogey or worse means dropping three points. A par does not affect the scoring.
Owen, 45, has taken the lead in Reno, Nevada, on the back of two consecutive 14-point rounds as he aims to end a run of 264 events without a victory on the PGA Tour.
His closest rivals are American Derek Fathauer and Australian Stuart Appleby but Owen's lead could have been bigger if he had not lost three points with a double bogey on the final hole of his third round.
Belgian Thomas Pieters and American Zach Johnson share the lead after the third round at the Bridgestone Invitational in Akron.