After defeating Spain’s Paula Badosa 7-6 (7-2) 7-5, world number 10 Haddad Maia advanced to the quarterfinals.
The sixth seed broke Boulter in the eleventh game of set two before holding service to win the match after dominating a first set tie-break after an equal start.
The 28-year-old Briton, who defeated Sara Errani in her opening round after losing in the first round of the Wuhan Open last week, is suffering her first defeat to Brazil’s Haddad Maia in four matches.
Boulter, who holds three career singles titles, had a career-high ranking of 35th in the world.
In other news, American Frances Tiafoe will play British player Dan Evans in the Almaty Open’s second round in Kazakhstan on Thursday.
