Romania's Halep, the world number two, downed Belgian Flipkens 6-4 6-2 in one hour 27 minutes at the WTA Premier event in Cincinnati.
Both players struggled on serve in the opening set, with 22 break-point opportunities shared between the two - with Halep taking the lead after saving a break point when serving for the set.
The match found more rhythm in the second set, with Halep inflicting breaks in games one and five and losing just four points on serve for the remainder as she cantered into the last 16.
Other second-round results saw fifth seed Maria Sharapova and 12th seed Caroline Wozniacki win their first matches in Ohio.
Russia's Sharapova was tested by American Madison Keys before winning 6-1 3-6 6-3, while Denmark's Wozniacki continued her solid form with a 6-2 6-3 thrashing of China's Zhang Shuai.
In first-round action, seeds Sara Errani (14), Carla Suarez Navarro (15) and Lucie Safarova (16) progressed with three-set wins.
Italian Errani was down a break in the third set against Belgium's Yanina Wickmayer but bounced back to win 7-5 3-6 7-6 (7-2).
Suarez Navarro of Spain was too good for Bulgaria's Tsvetana Pironkova 6-3 1-6 6-2, while Czech Safarova beat in-form American Venus Williams 6-7 (2-7) 6-3 6-4.
Czech Barbora Zahlavova Strycova won 11 consecutive games on her way past lucky loser Mona Barthel of Germany 7-5 6-0.
Zahlavova Strycova was set to play Victoria Azarenka, before the Belarusian withdrew from the tournament with a right knee issue.
American Sloane Stephens broke Germany's Andrea Petkovic five times on her way to a 6-3 6-3 win, and Japan's Kurumi Nara thrashed Swiss Romina Oprandi 6-0 6-2.
Qualifier Andrea Beck of Germany beat Spaniard Garbine Muguruza 6-3 2-6 6-3, and her countrywoman Sabine Lisicki defeated Italy's Roberta Vinci 6-3 2-6 6-2.
Russian Ekaterina Makarova was a 6-2 6-2 winner over Slovakian Daniela Hantuchova, and compatriot Svetlana Kuznetsova hit 12 aces in a tough victory against Italian Camila Giorgi 6-4 6-7 (4-7) 6-3.
Wildcard Christina McHale won an all-American battle against qualifier Nicole Gibbs 4-6 6-3 6-1.
Kazakhstan's Zarina Diyas edged out fellow qualifier Irina-Camelia Begu 7-6 (7-4) 7-6 (7-5).