The top-ranked Ko edged Menendez 3 and 2 on Thursday at Club de Golf Mexico in the event that switched from stroke to match play and from November to April.
''I am going to try to give myself as many birdie opportunities as I can,'' Ko said. ''I think a big key going forward is that you need to have many birdies opportunities, because some of them will end up falling.''
Third-ranked Ariya Jutanugarn will face older sister Moriya in the second round.
''I think playing against her will be fun, because even if I don't make a putt in that hole and she does I'll feel happy for her,'' Ariya said.
Ariya beat Amy Anderson 5 and 4, and Moriya topped Alena Sharp 2 and 1.
''Is a little too early this week to see my sister, but ... tomorrow will be fun,'' Moriya said.
Ko will face Jennifer Song, a 3-and-2 winner over Mi Hyang Li.
Ko took a two-hole lead with birdie win on the par-5 second and par-4 fourth. Menendez took the par-3 fifth with a birdie, and Ko rebounded with birdies on the par-4 seventh and eighth to make it 3 up. Menendez won the par-5 10th with a birdie, Ko took the par-3 14th with a par and ended the match with a birdie halve on the par-3 16th.
''Hopefully, that last birdie is good momentum going into tomorrow,'' Ko said.
The event is the LPGA Tour's first match-play tournament since 2012.
Carlota Ciganda, the November winner in stroke play at Club de Golf Mexico in the then-Lorena Ochoa Invitational, topped Mexico's Gaby Lopez 5 and 3.
''I love match play,'' Wie said. ''It reminds me of Solheim Cup. It brings back lot of memories. I love it. I had fun today and Lizzete was a really good opponent. I chipped down for eagle twice.''
Wie will play Laura Gonzalez Escallon, the Belgian player who knocked off fourth-ranked In Gee Chun 2 and 1.
Cristie Kerr topped Brittany Altomare 2 and 1. Kerr won three weeks ago in Hawaii and lost to Haru Nomura on Sunday on the sixth hole of a playoff in Texas.
''I didn't really have my full game today and I still got it done,'' Kerr said. ''I made some really clutched-outs coming in and I was able to get it done.''
Olympic champion Inbee Park beat Peiyun Chien; Shanshan Feng had a 7-and-5 victory over Laetitia Beck; and Brooke Henderson outlasted Katherine Kirk in 20 holes. Stacy Lewis dropped a 1-up decision to Ayako Uehara.