The Swiss world No 3 was runner-up to Roger Federer at Indian Wells last weekend and with both Andy Murray and Novak Djokovic missing out in Florida through injury, he is the top seed in Florida this week.
And the three-time Grand Slam champion justified that position with a masterful display to beat world No 75 Zeballos for the lost of just seven games.
Having saved break points in the opening game of the match, Wawrinka never looked back as he fired 24 winners, including eight aces, and lost just 13 points on his own serve to advance to the third round.
"I'm really happy, I think it was a great match, especially for the first one here for me," Wawrinka told the ATP's website and he will next face either Malek Jaziri or Feliciano Lopez.
"It's quite tough conditions, raining and really windy today. It is really windy on the court, so it is never easy.
"I'm happy with the way I was moving, the way I was playing and my attitude in general was really positive. So it's a great match.
"I'm playing better tennis. I feel that I'm playing good here. I took the confidence from Indian Wells. So let's see, when I'm playing well, when I am confident with my game, I know I can beat anybody."
With 10 seeds crashing out of the bottom half of the draw on Friday night, the big guns in the top half flexed their muscles in the early Saturday action.
David Goffin, a semi-finalist in Miami last year, had little trouble in booking his third round spot, seeing off Barbadian qualifier and world number 121 Darian King with a 7-5 6-1 success.
The world No 11 and eighth seed will next face Diego Schwartzmann after the Argentine claimed the scalp of 27th seed David Ferrer with a straight sets triumph.Tomas Berdych, runner-up to Andy Roddick in Miami in 2010, proved too strong for Russian teenager Andrey Rublev.
The 10th seed beat the 19-year-old 6-3 6-2 to set up a big-hitting clash with Luxembourg's Gilles Muller, who got the better of Andreas Seppi in a match that featured not a single break of serve.
Muller did the damage when it matter, claiming both tie-breaks to reach the third round and match his best showing at a Masters - he also reached this stage in Indian Wells last week and in Canada in 2015.
Sam Querrey, the 22nd seed, also advanced thanks to 6-2 6-3 win over Tommy Robredo in just 52 minutes.
