The 19-year-old Azarenka, who saved a set point in the first set, improved to 1-2 against the fourth-seeded Russian.
"I just kept on fighting,'' said Azarenka, who grunted loudly on almost every point. "We had many long rallies, I tried to fight for every ball. I played very well.''
Azarenka will next play another Russian, Nadia Petrova, who beat Li Na of China 6-2, 6-3. Petrova, the 2006 champion in Stuttgart, clinched the match with an ace.
Dementieva made too many errors in the third set, allowing Azarenka to race to a 5-0 lead. Dementieva saved three match points to win her first game, but then made two straight errors and put a backhand into the net to lose after nearly three hours.
Azarenka hasn't won a tour title while Dementieva has 10, including at Dubai and the Beijing Olympics. The Russian has returned to her highest ever ranking of No. 4, which she also reached three years ago. Azarenka is ranked No. 17.
Maniche Suffers Back Injury
WCQ Preview: Spain - Armenia
Dementieva charges into U.S. Open semis
Maniche Suffers Back Injury
WCQ Preview: Spain - Armenia
Dementieva charges into U.S. Open semis
