A five-time winner of the elite event, the American fired down six aces and broke her opponent four times on the way to a one-sided victory in her first appearance since the Australian Open in January.
"I'm always a little nervous in the first round, and I kind of chill out after that," 10th seed and former world number one Williams said. "It's always the same. It's always been the same.
"Last time I played I played horrible, and I was thinking as long as I don't hit a ball into the stands I'll be good. I didn't do that today, so it worked out well."
Williams, who won the title in Miami in 2002, 2003, 2004, 2007 and 2008, had not played in the event since 2009 because of injury and illness.
The 13-time Grand Slam singles champion will next face Italy's
"With these weather conditions it's tough serving," Clijsters said. "I don't think there's anybody who plays a whole tournament with perfect tennis, so you have to try and battle through, find the solutions when you're not playing your best.
"Mentally, that's one of the biggest focuses I have when I step out on the court here in Miami, where it can get very windy."
Clijsters is playing in her first tournament since she lost to eventual champion Victoria Azarenka in the Australian Open semi-finals when she injured her ankle.
In other matches on Thursday, second-seeded Russian
The Serbian world number 15 was whitewashed in the opening set on her way to a 6-0 6-3 thrashing at the hands of the world number 36.
Jankovic offered her opponent just four break points during the 61-minute encounter, but Barthel was ruthless as she took every one of those chances - and equally nerveless in defending all four break points Jankovic earned in reply.