The Ryder Cup star carded a two-under 70 to reach six under, but his advantage would have been greater had it not been for a bogey at the last after missing the green and then firing his chip 25 feet past the hole.
Dubuisson's momentum was halted after he birdied the 15th to move three clear when the threat of lightning forced a two-and-a-half-hour suspension.
By then second-placed South African Darren Fichardt, who was not even in the field Thursday morning but got in as a late reserve, and Lee Westwood were safely home in the clubhouse on four under after rounds of 69 and 70 respectively.
Windier conditions made scoring more difficult than the opening day with just 12 under-par rounds posted.
Ireland's Shane Lowry, starting at level par, coped best and was five under through 10 holes only for one dropped shot at 11 to be followed by a triple-bogey eight at the 14th as he eventually finished one under.
That put overnight leader Bernd Wiesberger back in front only for the Austrian to leak three shots in two holes early in his round to leave Dubuisson two clear at the top on six under. Wiesberger failed to recover from that slip and carded a five-over 77 to drop out of contention.
Race to Dubai leader Tommy Fleetwood shot a 74 to slip to three over to leave him with the remotest of chances of clinching the title with a win this week.