Halep reached the Cincinnati quarters for the fifth straight year, contesting the final in 2015 and the semi-finals last year in the hardcourt run-up to the U.S. Open.
She can leapfrog Karolina Pliskova as world number one by winning the title, which the Czech won last year.
Pliskova led Camila Giorgi of Italy 3-0 in the first set before rain suspended the match.
Halep trailed 4-2 in the opening set against Latvia's 15th-seeded Sevastova, who was aiming to take a set off the Romanian for the first time in their last four meetings.
But Halep reeled off the last four games to take the set, helped by Sevastova's unforced errors on crucial points, and won the first three games of the second set on her way to victory.
"The match felt quite tough, it was not easy at all," said Halep, who will face Johanna Konta in the quarter-finals.
"I won against the 15th player in the world playing not as I want. It's a big thing, and I'm really happy about it."
With American Madison Keys serving, Garbine Muguruza saved three match points before breaking and sending the match into a third-set tie breaker, where the Wimbledon champion prevailed.
Muguruza's 6-4 3-6 7-6(3) victory set up a quarter-final against Kuznetsova.
(Reporting by Larry Fine in Tampa and Rory Carroll in Los Angeles; Editing by Ken Ferris/Peter Rutherford)
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