The Belgian was one of the last players to finish on day one, taking 90 minutes to beat her opponent 7-5 6-4 this evening.
The players were well matched at the start of the first set, with neither losing a break point in the opening 10 games.
However, the 20th seed had a chance to edge ahead in the 11th, with Puntintseva struggling with her serve, allowing Flipkens to take the first break of the match before serving out the set.
Puntintseva's serve was stronger in the second set, but Flipkens was able to up her game, smashing a series of winners past her opponent to gain a break and wrap up the match.
Flipkens will play Bojana Jovanovski in the second round.