Tauson raced into an early lead on the back of a strong service game while Andreeva made two double faults to quickly find herself 2-0 down but the Russian quickly recovered and began playing her shots, breaking back to level at 2-2.
Mirra Andreeva became the youngest player to win a WTA 1000 title when the 17-year-old beat Clara Tauson 7-6 (1), 6-1 in the Dubai Tennis Championships final on Saturday.
Andreeva, who is coached by former Wimbledon champion Conchita Martinez, then dictated rallies and began grinding down her opponent, firing winners with emphatic overhead smashes that left Tauson deflated as the Russian teenager went 5-1 up.
Rublev broke twice early on to storm into a 5-0 lead and while Draper avoided a bagel, the Russian fired down two aces to wrap up the win.
Andreeva has yet to lose one this year and she was near-perfect as she won the first six points before taking the opening set when Tauson sent a return long.