The 25-year-old Kaur, competing in qualification B, sent the discus to a distance of 64m in her third and final attempt to be one of the only two automatic qualifiers for the final round, the other being American Valarie Allman (66.42m).
The final will held on August 2.
The Indian ended ahead of defending gold-medallist Sandra Perkovic (63.75m) of Croatia and reigning world champion Yaime Perez (63.18) of Cuba. Perkovic qualified at third and Perez at seventh.
But veteran Seema Punia made an exit after finishing sixth in qualification A and 16th overall with a below-par best throw of 60.57m.
Kaur began with a 60.29m effort and then improved it to 63.97m before her third throw of 64m. Every competitor gets three throws.
Those who touch 64m or at least 12 best performers in the two qualifying rounds advance to the final.
The Punjab athlete has been in impressive form this year as she breached the 65m mark twice recently.
She threw 65.06m during the Federation Cup in March to break the national record and become the first Indian to breach the 65m mark.
Then in June, she bettered her own national record with a throw of 66.59m during the Indian Grand Prix-4 to sit at world number six.
Season leader Jorinde van Klinken of Netherlands failed to make the final round cut with a modest throw of 61.15m.
She has a season’s best of 70.22m while Allman is second best this year at 70.01m.
Punia, who had booked a last minute Olympics berth, was way below her season and personal best marks.
She fouled her first throw and had 60.57m and 58.93m in her next two attempts to make an exit from what would be her last Olympics.
The 38-year-old Haryana athlete had made it to the Olympics on the day of qualification deadline with a throw of 63.72m during the National Inter-State Championships in Patiala on June 29.
She has a personal best of 64.84m, a performance she produced way back in 2004.
She returned to action only this season after appearing for the 2018 Asian Games in Jakarta where she won a bronze.
Punia has been training outside the national camp, mostly in Russia and neighbouring countries. She had come to Tokyo with her personal coach Alexander Sinitsyn who was with her in Jakarta.
It was the veteran discus thrower’s fourth Olympics. She has never qualified for the final round.
She made her Olympic debut in 2004 in Athens where she had a best throw of 60.64m. In 2012 and 2016 Olympics, she had disappointing performances of 61.91m and 57.58m.
Punia has won laurels for the country in the Commonwealth and Asian Games.
She has won a medal each in all four CWGs since 2006 — three silver and one bronze in all.
She also won a gold and a bronze in the 2014 and 2018 Asian Games respectively.