Ten-time grand slam champion Williams, who has not played a WTA event since pulling out of last year's US Open, defeated Japan's Kimiko Date-Krumm 6-0 6-3 in 77 minutes at the Miami WTA/ATP event.
"It was definitely a bit nerve-wracking ... but I was able to get a great start and settle in and play well against a really difficult opponent. It was definitely an ideal start."
Williams announced at last year's US Open she had been diagnosed with the auto-immune disorder Sjogren syndrome, an illness that saps her energy and causes pain in her joints.
"Just to be in this tournament is a huge win for me," Williams said.
Williams, who played doubles for the US Fed Cup team last month, pulled out of last year's US Open after a first-round victory.
Clijsters, who won at Miami in 2005 and 2010, skipped last week's Indian Wells tournament to rest her injured ankle, the latest in a list of ailments in the past year that has also included a sore shoulder, wrist and abdomen.
"It's just a matter of getting those matches again," Clijsters said. "One thing I can count on is I have the experience, though. It doesn't take me that long to get used to it again. But it has become tougher."
Saying her ankle is at 95 per cent of peak fitness, Clijsters pondered how close she came to knocking off top seed Azarenka in Australia and how strong Azarenka - now undefeated this season in 23 matches - has played.
"I felt like I was really close to winning that match (at Melbourne Park)," Clijsters said. "She has been playing really good tennis. I think she's in a state of mind where she feels very confident and is on a roll.
"It's really showing in her game and in the way she approaches matches. I know what it's like to be in that situation, where you feel very focused but at the same time playing freely, without any worries."
Williams advanced to a second-round match against Czech third seed, and Wimbledon champion Petra Kvitova, who had a first-round bye. Next up for Clijsters is her match against Germany's 14th-seeded Julia Goerges.
First round matches began in the men's draw with Russian Nikolay Davydenko outlasting American James Blake 4-6, 6-4, 6-4, to book a second-round date with US 10th seed John Isner, the runner-up to Roger Federer last week at Indian Wells.
Colombia's Alejandro Falla was leading 6-1, 2-1 when Uzbek Denis Istomin retired with an injury, advancing the South American into a second-round match with British fourth seed Andy Murray.