The Russian appeared certain to slip to a frustrating defeat after squandering numerous break-point chances, however she saved two match-points in a second set tiebreak before mounting a stunning comeback.
It was a lengthy and dramatic affair that finished just shy of midnight local time, and Kasatkina has little time to recover before encountering her compatriot Elena Vesnina on Thursday.
Konta accepted a wildcard into the tournament in an effort to get some much-needed match-time, but her stay in Dubai has been cut short. It was yet another scratchy performance from the 26-year-old – and uncharacteristic unforced-errors continue to plague her game.
The British No.1 made an eye-watering 65 mistakes against her second round opponent, and even her trusty backhand showed signs of frailty.
Kasatkina, who ended Caroline Wozniacki’s winning streak in St. Petersburg earlier this month, was left frustrated in the first set due to her inability to convert her chances.
The 20-year-old had ample opportunities to move a break of serve ahead – seven in total – but she failed to seize the initiative. Konta had remained resolute under pressure, and she achieved a 4-3 advantage when her opponent nudged an attempted backhand passing-shot into the tramlines.
Kasatkina could scarcely believe she had slipped a break behind after so much good work, and she was unable to muster a response as the Brit snatched the first set.
The second set ebbed and flowed, but a tiebreak was required to settle the outcome. Konta’s serve helped her carve open two match-points, but her backhand misfired when she needed it most.
Kasatkina had battled back from the brink of defeat, and she converted her first set-point after a breathless exchange. A piercing backhand winner down the line was initially called out, but Hawk-eye came to the Russian's aid.
Konta took a lengthy bathroom break before the third set commenced, but she was unable to stay with her on-song opponent. The Brit picked up just two more games as her time in Dubai came to an unsatisfactory end.
Earlier in the day, there were victories for Elena Svitolina, Naomi Osaka, Karolina Pliskova, Angelique Kerber and Caroline Garcia.