Just over a year ago, the Scot was unranked, but after winning four consecutive Challenger titles, he has surged into the top 100.
After taking a few weeks off, the 23-year-old advanced to the main draw of the ATP 250 event in Sweden by winning two qualifying sets.
He advanced to face Dutch seventh seed Tallon Griekspoor in the second round after defeating Moutet of France 6-2 7-6 (7-5).
Fearnley, who received a wildcard and triumphed in the first round of Wimbledon in July, is winning at the ATP Tour level for the second time.
According to ATP records, Fearnley’s ascent to 98th place in the world—from 1,893rd in September 2023 and 646th in the beginning of this year—is the fourth largest ascent into the top 100 since 2000.
Cameron Norrie began his recovery from an arm injury at the same event, losing 6-4 6-4 to Miomir Kecmanovic of Serbia.
In another match, Dan Evans advanced to the second round of the Almaty Open in Kazakhstan by defeating Taro Daniel of Japan 6-2 7-6 (7-4).
At the Ningbo Open in China, British women’s number one Katie Boulter also triumphed, defeating Italian veteran Sara Errani 6-3 6-2 after a rain delay.