Fisher carded an even-par 71, 10 strokes more than his previous round, thanks to the rough stretch in which he was 4-over. Still, his 54-hole total of 12 under 201 was good enough for a one-shot lead.
Fisher was coming off a tournament-record-matching 61 on Friday.
Knotted in second place were Chris Wood (66) and Francesco Molinari (69) at minus-11. Gonzalo Fernandez-Castano was neck-and-neck with them until he carded a double-bogey on the 18th and fell to fourth place at minus-10.
Tied for fifth at 9-under 204 were Richard Green (69) and Padraig Harrington (69).