Wimbledon champion Halep, seeded fourth, earned a late break in the penultimate game of the final set to reach the third round after two hours of action.
The Romanian has finished runner-up in Cincinnati three times, last reaching the final a year ago against Kiki Bertens.
In the next round, the 27-year-old, who retired injured from her Toronto quarter-final against Czech qualifier Marie Bouzkova last week, will face either Madison Keys of the United States or Russia's Daria Kasatkina.
"It was a very, very tough match," Halep said. "She played well, hitting the ball very strong.
"Mentally, it was tough to return for me at the start after playing injured last week.
"But I didn't have pain, which is good. It took time to get a rhythm and then do something on court."
She went up a break in the third set, before letting the lead slip, only for the 43rd-ranked Alexandrova to serve two straight double-faults and fall 5-4 behind.
Halep completed her fightback on a second match point a game later.
"After the first set, I felt I could play aggressive," she added. "I also changed the tactics.
"I fought and did not give up. I wanted to run for every ball, it felt really good."
Ninth seed Elina Svitolina, a semi-finalist four years ago, advanced past Belgian Elise Mertens 6-4, 6-1.
In the men's draw, Kei Nishikori lost to fellow Japanese Yoshihito Nishioka 7-6 (7/2), 6-4.
Sixth seed Nishikori has still never advanced beyond the third round in Cincinnati.
France's Richard Gasquet, who ended Andy Murray's comeback singles tournament in the first round, saw off Argentinian Federico Delbonis 7-5, 7-6 (7/1).
Australian Alex de Minaur defeated American Reilly Opelka 7-6 (7/3), 6-4 to set up a third-round tie with Nishioka.
Results on Wednesday in the WTA/ATP Cincinnati Masters (x-denotes seeding):
Richard Gasquet (FRA) bt Federico Delbonis (ARG) 7-5, 7-6 (7/1)
Yoshihito Nishioka (JPN) bt Kei Nishikori (JPN x6) 7-6 (7/2), 6-4
Alex De Minaur (AUS) bt Reilly Opelka (USA) 7-6 (7/3), 6-4
Aryna Sabalenka (BLR x9) bt Zheng Saisai (CHN) 6-4, 6-3
Elina Svitolina (UKR x7) bt Elise Mertens (BEL) 6-4, 6-1