With a completely bogey-free round of 66, six under par, he climbed 26 places during the third round on Saturday. He was tied for eighth at the Cadillac Championship in Miami.
Norén shared second place for a while with American Ben Griffin. On the ninth hole, he had a birdie putt that stopped right at the edge of the hole.
He failed to gain any strokes over the final nine holes and remained at minus three for the day and minus ten overall (74-69-66-69).
Norén has never won on the PGA Tour, but has finished second three times and third twice as often.
American Cameron Young had an excellent weekend, winning by six strokes over world number one Scottie Scheffler.
Ludvig Åberg did not play in the competition.
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