Thompson, with a wind of 0.9m/sec, took the title in Kingston with Oblique Seville second in 9.82 and Ackeem Blake third in 9.92 to book their trips to the Paris Olympics.
Thompson, 22, improved upon the year's prior best, a 9.79 by Kenya's Ferdinand Omanyala two weeks ago in Nairobi.
After not racing all season, Thompson cruised in the Jamaican trials, running 9.82 in Thursday heats and 9.84 in the semi-finals earlier on Friday.
Thompson withdrew before last year's semi-finals in the qualifying meet for the World Championships despite a 9.86 qualifying run, but he later ran 9.85 at a Diamond League meet in Xiamen then went 9.87 at Eugene.
Jackson, a two-time 200m world champion and two-time 100m world runner-up who was third in the 100 at the Tokyo Olympics, won the women's 100 in 10.84secs (-0.3 m/sec wind).
An injury had knocked out reigning Olympic champion Elaine Thompson-Herah, the 100 and 200 gold medal winner at the Rio and Tokyo Games.
The final runner-up was 19-year-old Tia Clayton in 10.90 with 37-year-old Shelly-Ann Fraser-Pryce third in 10.94 to book her trip to Paris.
Fraser-Pryce, the 2008 and 2012 100m Olympic champion ran 10.91 in the semi-finals before grabbing her spot smoothly in the run for France.
