Fleetwood had birdied the first from 15 feet and then eagled the long second, but a bogey at the sixth saw him fall back into a share of third with home favourite Stephen Gallacher.
There was a three-way tie at the top when Fleetwood birdied the eighth, ninth and tenth, Wiesberger picked up shots on the seventh and ninth and Gonzalez also birdied the par five ninth.
But Wiesberger then three-putted the par three tenth to drop back to 15 under.
Gallacher was finally overtaken as clubhouse leader, some two and a half hours after he finished, when Sweden's Fredrik Andersson Hed birdied the 18th to complete a 66.
At 15 under par, he was two behind leader on the course Fleetwood, who had holed from five feet for birdie on the 13th and then got up and down from a greenside bunker on the par five 16th.