After a steady start to her round at the Ritz-Carlton Golf Resort, the Paraguayan burst into life at the seventh with her first birdie of the day at the par four.
Another four followed in the next seven holes to see her jump to the top of the leaderboard, a final birdie at 17 completing her round and setting things up nicely for the tournament.
Sandra Gal is Granada's nearest competition after carding 68, while Belen Mozo and Caroline Hedwall are tied for third a further shot back.
With vital Race to the CME Globe points on offer at the tournament, the top three in the standings all had solid starts to the tournament.
Current leader Stacy Lewis is with Mozo and Hedwall on three under, while her nearest rivals Inbee Park and Lydia Ko are two shots back in a group of nine players on one under.
Lewis' round had not been spectacular with two birdies and a bogey by the 16th, but an eagle three at the par-five 17th saw her leap up the leaderboard.
Ko had been in good shape until the 15th when back-to-back bogeys saw her drop to even par, but a birdie on 17, proving a popular hole, saw her finish under par.
Park's day started with a bogey at the second but she quickly moved back to level par, picking up a shot at the fourth.
She had to wait until the birdie-laden 17th to move under par though, the South Korean getting up and down in four to keep herself close to Ko.