Last year, Babos upset a number of higher-ranked opponents, including Sorana Cirstea and Sara Errani, to win her maiden WTA tournament, and, despite a few pre-match nerves, she reveled in her role as defending champion, wrapping up a 63 63 victory after little over an hour on court.
"I really had to push myself on court today and felt a little bit of pressure, which I had never really felt before at a WTA tournament," Babos said after the match. "Ana played good tennis today and she's a lefty so it was a little bit uncomfortable for me and I'm just really happy to get through this first round.
"I loved being on the center court here again, I love playing in front of this crowd and I enjoyed every moment today."
Wickmayer, the No.6 seed, arrived in México with just one win from her past three tournaments, and she was made to work hard against Valeria Savinykh, eventually coming through, 46 61 64.
Niculescu, meanwhile, had a far easier time of things against Kimiko Date-Krumm, who, trailing by a set and a break, retired midway through the second set due to a back injury.
"First rounds are always tough because you need to get used to the court," Radwanska said. "This is my second time here, although the other time was four or five years ago. It's definitely faster here than in Miami and the balls are flying a lot because of the altitude.
"But I played a very good first set and the second set she just came back stronger and she was playing more aggressive. Then in the third set I came back! I started to play my tennis again and it got me through in the end."