This record is for most consecutive birdies at the end of a tournament to win that event on the PGA Tour.
6
Mike Souchak, 1956 St. Paul Open (last 6 holes)
5
Jack Nicklaus, 1978 Jackie Gleason Inverrary Classic (last 5 holes)
Tom Weiskopf, 1971 Kemper Open (last 4 holes plus 1 playoff hole)
John Cook deserves mention here, too: He had a five-hole streak that involved four birdies and an eagle to win. It happened at the 1992 Bob Hope Chrysler Classic. Cook birdied the last hole of regulation, then the first three holes of the playoff, then ended the playoff with an eagle on the fourth hole.
Source: PGA Tour

