Fisher birdied the 10th and 13th holes, and then carded an eagle on the 15th before making back-to-back birdies on Nos. 16 and 17.
The Briton, seeking his fifth European Tour win, finished the first two rounds at 13-under 131.
Morten Orum Madsen matched him with a 65 to claim sole possession of second place at 12-under.
Overnight co-leader Simon Dyson (68) and Carlos Del Moral (65) shared third place one shot further back.
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