She was born into a poor family, to Vasili Andreevich Engelhardt, captain of the Smolensk gentry (1735–1794) and Martha (Elena) Alexandrovna Potemkina (1725–1775), the sister of Grigory Potemkin, lover and possible husband of Catherine the Great.

At court, Tatiana attracted attention not only as the niece of the most powerful nobleman in Russia, but also due to her intelligence, beauty, and lively attitude.

The Duchess of Kingston who visited Saint Petersburg and joined the court in 1777, became attached to the then fifteen-year-old Tatiana, treating her like a daughter.

On 11 September 1785, Tatiana married a distand relative, 25 years her senior, Lieutenant General Mikhail Sergeevich Potemkin (1744–1791).

Soon she met nobleman Prince Nikolai Borisovich Yusupov, who had recently returned from Italy where he was stationed at the embassy.

She lived with Praskovya Grigorievna Lupolova, the daughter of an exiled man who had come to the capital to seek mercy for her father and found the patronage of Yusupovna, Daria Trubetskaya, and Avdotya Golitsina.

Her great-great-grandson, Prince Felix Yusupov, described her in his memoirs:Princess Tatiana was not only a perfect hostess, as gracious as she was witty, but also proved to be an excellent businesswoman.