Jones, who tops the junior girls' world rankings, pushed world No.9 Kasatkina all the way in their Adelaide International meeting on Wednesday night.
The 16-year-old won the first two games of the opening set without dropping a point but was eventually beaten 7-5 6-3 by her vastly more experienced opponent.
Kasatkina, a French Open semi-finalist and Wimbledon quarter-finalist, was troubled at times by Jones' clean and powerful ground strokes.
"It was a pretty intense match," Kasatkina said post-match.
"I'm really happy with how I was able to come back after a very quick beginning, let's say, of the match.
"She's got really good tennis, so I'm already a bit scared, to be honest. She's just 16 (years old)."
Jones has already drawn comparisons with three-time major champion Ash Barty and won plenty of admirers this week in Adelaide, where she banked her first win over a WTA top-50 ranked player.
The Gold Coast youngster swept aside China's world No.37 Wang Xinyu 6-4 6-0 in the opening round.
Kasatkina will continue her push for a ninth career WTA title when she faces American world No.20 Madison Keys in the Adelaide quarter-finals.
The 27-year-old has twice reached the final in Adelaide, losing to Jelena Ostapenko last year and Belinda Bencic the previous summer.
Kasatkina's attention will then turn to the Australian Open, where she has twice reached the third round, most recently in 2022.
"To achieve the final stages of the tournament is always a good sign, so I'm happy with the first quarter-final of the year," Kasatkina said.
22°C