Johnson began the day with a five-shot lead over a top-class field featuring 40 of the world's top 50 after equalling the course record at Sheshan International with a second round of 63.
That lead was down to two shots when Poulter, whose victory 12 months ago came at Mission Hills, carded five birdies in a row from the third to move to 11 under par.
However, Johnson was almost equally impressive over the same stretch of the course, picking up shots on the third, fifth, sixth and seventh to briefly restore his five-shot advantage.
Poulter, looking to become only the second player after world number one Tiger Woods to defend a WGC title, holed a long, curling birdie putt on the ninth to complete a front nine of 30 and reduce the gap to four, only for Johnson to birdie the par-five eighth.
Back came Poulter with yet another birdie on the 10th and the leading duo were threatening to pull away from the field, with Germany's Martin Kaymer three shots further back despite being an amazing 10 under par for his round.
The Ryder Cup star began the day 12 shots off the lead on level par but, having started from the 10th, covered the back nine in 30 before picking up further shots on the second, fourth, fifth and sixth.
That meant he needed to birdie his last three holes to shoot the first ever 59 on the European Tour, while three pars would be good enough for a course-record 62. Kaymer already holds a share of the record after his win here in 2011.
Canada's Graham DeLaet and Northern Ireland's Graeme McDowell were a shot behind Kaymer on nine under, with US Open champion Justin Rose, Sergio Garcia and Rory McIlroy all another stroke adrift.