Poulter, 34, started the day with a two stroke advantage over the rest of the field but made a slow start on the Fanling course as he dropped a shot for the first time at the tournament on the par five third, with his tee shot finding the greenside lake.
He recovered though with three birdies over his next four holes moving him onto two under for the day and 21 under for the tournament at the turn.
Dyson, meanwhile, was waiting to pounce on any further slip-ups from Poulter with the Yorkshireman one stroke behind after nine holes.
The former Asian Tour Order of Merit winner carded an eagle three on the third before immediately adding a birdie on the next hole.
Dyson added further gains on the sixth and seventh holes to move briefly alongside Poulter before putting for bogey on the eighth to move onto four under for the day and 20 under overall.
Graeme McDowell had started the day as Poulter's closest challenger but the Northern Irishman will need to up his game on the back nine having dropped shots on the first and third before making par on the rest heading out.
The US Open Championship winner was two over through nine and six shots behind Poulter.
Rory McIlroy too was seeing his chances of victory slipping away with the 21 year old one under through nine and trailing Poulter by five.
Anthony Kang was keeping himself in touch with the leaders with the American three shots off the pace at three under after nine holes while Gareth Maybin was the day's biggest mover with the 30 year old from Northern Ireland carding a nine under 61 after mixing his scorecard with an eagle, nine birdies and two bogeys.