Each gamers misplaced their serve thrice within the first set however Boulter dominated the tie-break to take a bonus.
Boulter improved considerably within the second set, when she received 78% of factors on serve in comparison with 51% throughout the first set.
The victory was much-needed after a disappointing summer time.
The 29-year-old got here into the match on the again of 5 opening-round defeats from seven tournaments, slipping behind Sonay Kartal within the rankings to turn into Britain’s quantity three.
Cirstea got here from behind to beat Japan’s Moyuka Uchijima 2-6 6-4 6-2 to arrange the match towards Boulter.
Prime seed Naomi Osaka strolled into the second spherical with a complete 6-0 6-4 win towards Sonobe Wakana.
