Fleetwood (67) birdied the last hole of regulation to match Rai’s total of 11 under par, but then missed from three feet for par on the first extra hole.
“Tommy had finished off incredibly and it’s not nice to see him miss that but it feels incredible,” said Rai, who won the 2018 Hong Kong Open and finished second in the Irish Open seven days ago.
The 25-year-old Rai had set the clubhouse target after a superb 7-under 64, recovering from a bogey at the second to birdie five of the next six holes before picking up three more shots on the back nine.
Robert Rock (70) looked set to match Rai’s total after he birdied Nos. 10, 13, 15 and 16, only to bogey the last after a clumsy chip from just short of the green.
Herbert held a one-shot lead at the halfway stage but slumped six shots off the pace following a third round of 79 in miserable conditions on Saturday.
However, the 24-year-old Herbert surged into the lead with six birdies in the first 10 holes Sunday and recovered from a bogey on the 12th with further gains on the 15th and 16th, only to crucially drop a shot on the 17th.