Granada combined with Celeste Troche to shoot a 5-under 139 in the singles format, giving the two-woman Paraguayan team a commanding advantage over second-place South Korea.
Ji Yai Shin and Young Kim were the only other players who combined to break par, posting a 1-under 143 at Gary Player Country Club.
The remaining 20 teams -- including Americans Pat Hurst and Juli Inkster -- will head into Saturday's foursomes carrying hefty scores after a challenging first round.
Granada and Troche were over-par for just two holes when Troche's double-bogey at the par-5 fifth left them a combined plus-one.
But Troche, six years the senior to 20-year-old Granada, rallied with back-to-back birdies at the seventh and eighth and her partner added another at the ninth to move Paraguay to 3 under.
Granada bogeyed No. 10, but the duo collected two birdies at the 11th and were already moving well clear of the field.
Troche closed out her round with two birdies, at 12 and 18, to shoot at 3- under 69. Granada had a birdie at 15 and another bogey at 17 to post a 2-under 70.
'Our goal was just to have fun,' said Troche, a non-exempt player on the LPGA Tour. 'We practice and play a lot together so we know each other and our games. It's all about having fun. If you can enjoy yourself and enjoy each other's company, that's what it takes.'
Added Granada, who won $1 million at the ADT last season, 'We're just going to go and have fun and hit the best shots we can. We're not going to get upset with each other.'
Italy and Scotland carded 1-over 145s to share third place -- one shot ahead of New Zealand (146) and two in front of Australia (148) and Wales (148).
Hurst and Inkster posted a 5-over 149 for the United States and were joined in eighth place by the team from Denmark. They combined for nine bogeys in the round (Hurst had a 2-over 74, and Inkster was a shot worse).
The first two tournament champions, Japan (155) and Sweden (157), struggled mightily on Day 1 and are tied for 14th and 16th place respectively.
Rounding out the field are Finland and Taiwan (150); Brazil and England (154); Japan and Spain (155); France, South Africa and Sweden (157); Ireland and Norway (160); Germany (165); and Kenya (169).
Norway's Suzanne Pettersen retired due to sickness and was replaced by Lill Kristin Saether.
After Saturday's foursomes, the event will conclude Sunday with a better ball format.