Every had made the cut just once in his previous five tournaments, but the one time he played on the weekend he finished tied for fourth at the Colonial Invitation.
He did not make a bogey during the second round at the Old White TPC course and posted a 36-hole total of 9-under 131.
Those tied for second a shot back were Daniel Summerhays, Bill Lunde, Steven Bowditch, Johnson Wagner and Russell Henley, who is attempting to become the third multiple winner on the tour this year.
Tommy Gainey, who shared the first-round lead with Wagner, was among those at 7-under 133 while 19-year-old Jorden Spieth was part of the group at 134.
It took a score of 1-under 139 to make the cut and among those missing it was Phil Mickelson, who completed 36 holes at 142 thanks to a 74 he fired on Thursday.
John Daly withdrew during the second round and later said he would undergo elbow surgery that would put him out of action for three months.
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