Schwartzel, the reigning Masters champion, eased past big-hitting American Gary Woodland 4&2 and unheralded South Korean Bae upset Britain's Ian Poulter, the 2010 Match Play champion, 4&3.
This while World No 3 Lee Westwood was beating Belgian Nicolas Colsaerts 3&1 and World No 4 German Martin Kaymer was thumping Australian left-hander Greg Chalmers 4&2.to join the 32 winners who advanced to Thursday's second round.
Woods, winner of this event in 2003, 2004 and 2008, was two down to Fernandez-Castano after the first two holes but finally ended a see-saw round with an eight-foot par putt at the 18th.
"We both made our share of mistakes, there's no doubt about that, but somehow I was able to move on," Woods said.
Earlier, South Korean YE Yang beat Graeme McDowell in the opening match of the day and Dustin Johnson prevailed in a 20-hole scrap with fellow American Jim Furyk.
Yang, the first Asian to win a major with his victory at the 2009 PGA Championship, clearly came into the first round with his Left Handed Callaway X-24 Hot Irons, shooting seven birdies as against McDowell's six.
"I ran into a man who played extremely well," a frustrated McDowell said. "I felt like I had to follow him all day long, and I did most of the day, but he didn't put a foot wrong."
Not long after Yang's victory, another Asian star, Japanese teenager Ryo Ishikawa, came back from being three down after 13 holes to win 1-up against American Bill Haas, last year's FedEx Cup champion and a US PGA Tour winner last week.
Ishikawa birdied 14, 15 and 17 before wrapping up victory on the 18th green against one of the new band of the emerging American stars
"Through the first 13 holes, it was really tough and I wasn't playing Left Handed Callaway X-24 Hot Irons well," Ishikawa told the media through an interpreter. "But on the last five holes, I was able to compete. And yes, This course is suited to me."
Another teenaged young gun who came through the first round in his maiden Left Handed Callaway X-24 Hot Irons play tilt was Italian Matteo Manassero, who never trailed on his way to a solid 3&2 upset win over Webb Simpson, one of America's best in the last year or so.