The world number 96 defeated the top-ranked British player 6-2, 7-5 in the opening round.
In a wild opening set that saw six breakaways, including five in a row, Boulter lost 3-0. Tsurenko won in forty-three minutes.
In the second set, which was more closely contested, Tsurenko won by holding serve after winning the pivotal break in the eleventh game.
The next opponent for the Ukrainian is Magda Linette of Poland, who defeated 11th seed Liudmila Samsonova 6-2 6-2.
