The tournament's 13th and 16th seeds respectively, Makarova and Petkovic both moved safely into the second round of the inaugural WTA Premier hard-court event.
Makarova will now take on either Stefanie Voegele or Timea Bacsinszky after brushing aside Bojana Jovanovski 6-2 6-2 in just over an hour.
The world number 14 sent down eight aces in a relatively straightforward success while Petkovic was made to work harder in her 5-7 6-1 6-2 triumph.
After being broken three times in the opener, Petkovic found another gear to quickly turn the match on its head, ensuring a tie with Samantha Stosur or Korea Open champion Karolina Pliskova.
Ukraine's Elina Svitolina also booked a second-round berth as the world number 35 defeated Camila Giorgi of Italy 6-2 6-3.
France's Carolina Garcia came through 6-4 4-6 7-6 (8-6) against Venus Williams while Alison Riske was 6-4 4-6 6-6 (5-0) up against Shilin Xu before the Chinese retired, apparently struggling with the stifling heat.
Klara Koukalova came unstuck against Zarina Dyas, the Kazakh qualifier prevailing 6-4 6-7 (1-7) 6-2 while Italian Karin Knapp will face third seed Petra Kvitova in the second round after seeing off Marina Erakovic 6-4 2-6 6-1.
There was no such joy for Knapp's compatriot Francesca Schiavone, who was a set and a break up before losing to 2-6 7-6 (7-2) 6-4 against Kirsten Flipkens.
Russia's Svetlana Kuznetsova was a 6-3 6-2 winner over Kurumi Nara of Japan, and Barbora Zahlavova-Strycova was given a strong test by the experienced Daniela Hantuchova.
The Czech saved six of eight break points she faced to win through 7-6 (7-5) 7-6 (7-2) and could face another Slovakian in the next round - with Dominika Cibulkova or America's Madison Keys waiting.