Fellow American Jennifer Capriati failed in her first match since November, losing 6-4, 7-6 to Greek Eleni Daniilidou, but top seed and defending champion Justine Henin-Hardenne claimed a comfortable 6-1, 7-5 win over Tunisian wild card Selima Sfar.
There were also victories for fourth seed Anastasia Myskina, fifth seed Ai Sugiyama and eighth seed Conchita Martinez.
Possessing a big serve and heavy groundstrokes, Molik proved a difficult opponent for Williams, who was playing only her fifth match after nearly seven months out injured.
Williams, who received a first-round bye, struggled with her first serve and her second was punished by some fine returns from the powerful Molik.
The American came under early pressure when she was forced to hold off two break points at 1-1. But Williams stole the only break of the set in the next game when Molik put a forehand wide.
Williams fought off a break point before holding for 4-4 in the second set and a weak service game from Molik allowed the 23-year-old to break to love and serve out for victory.
"It was one of my most exciting wins, to be honest," said Williams who made her comeback from an abdomen injury at the Australian Open last month where she lost to Lisa Raymond in the third round.
"I've never been so excited to win a first match because of all the hurdles I've been through. I really surpassed my expectations. I just feel really blessed that I was able to do what I did today."
Capriati competed well but was clearly lacking match tightness against the steady Daniilidou.
The American battled hard to stave off defeat, recovering from 5-2 and saving three match points in the second set.
But having broken to lead 6-5 she was unable to maintain her momentum and Daniilidou held her nerve to force a tiebreak which she swept through with the loss of just two points.
"She's a really tough player, and even when I've been in the best shape and playing well I've had tough matches with her," said Capriati.
"But it was a good test and I'm not too displeased with the way I played. Obviously I'm a little rusty, and it was just a few points here and there."
Daniilidou, who successfully defended her Auckland title in January, said her positive attitude was the key to her victory.
"Against the top players you have to play like this because they don't give you many opportunities," she said. "I was focused and moving well."
