The Australian went into Saturday's third round with a three-shot advantage, but he was able to extend that lead after producing a composed score of 68 that included five birdies.
The 33-year-old, who is chasing his second victory of his year following his triumph at the Arnold Palmer Invitational in March, has now moved onto 19-under-par for the tournament and he was pleased to maintain his momentum from the opening two days.
“The course changed quite a lot today compared to the first two days,” Leishman told the PGA Tour. “Firmed up a lot and the greens sped up, so that [good play] was good to see and nice to keep making birdies like I have been all week.”
Leishman's compatriot Jason Day and American Rickie Fowler are currently in a tie for second-place on 14-under, after they carded respective rounds of 70, while England's Justin Rose has moved into contention on 12-under following a bogey-free score of 66.
However, things did not go sell well for Rory McIlroy, who endured another frustrating day at Conway Farms Golf Club, as his third round score of 70 leaves him well off the pace on two-under, with his chances of retaining the FedEx Cup now all but gone.