The two-time Indian Wells champion Williams had a difficult time with Putintseva in the opening set but then steamrolled through the second to wrap up the win in one hour, 15 minutes yesterday.
"The first set was a little tricky, then I had to find my inner tiger, and roar," Williams said.
Williams moves on to the fourth round of the hardcourt tournament where she will face Kateryna Bondarenko who defeated Lesia Tsurenko 3-6, 6-4, 7-6 (9/7) earlier on Sunday.
Williams, who won the event in 1999 and 2001, returned to the tournament last year, ending a 14-year boycott which began after she beat Kim Clijsters in the 2001 final.
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That year spectators at Indian Wells booed Serena during the final and jeered her sister and father Richard Williams in the stands.
As the top seed and a 21 Grand Slam title winner, she's the clear favourite this week.
Although Williams got off to another slow start Sunday but she closed out in style with an ace on match point.
She needed a tiebreaker to win the first set, taking the final three points, including the last two on her serve.
"I was just trying to find my rhythm out there. Trying my best to not get off to a slow start," she said. "I was just trying to fight and do what I could."
The third seed from Poland needed just 87 minutes to eliminate Niculescu following a tough two-hour, 41-minute second round contest which she won 6-3, 3-6, 7-5 over Slovak Dominika Cibulkova.
"I knew I would have to be patient," Radwanska said of playing Niculescu. "I am just very happy to win that match in those two quick sets."
In men's action, Japanese star Kei Nishikori eased
through his second round match by beating Kazakhstan's Mikhail Kukushkin 6-3, 6-3.
The 26-year-old Nishikori, seeded fifth in his eighth appearance in Indian Wells, has never made it past the fourth round in the California desert.
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"It is not easy playing the first match of any tournament," Nishikori said. "But I felt comfortable today. So I hope I can go further than the last couple of years."
Nishikori, who has been ranked as high as fourth in the world to become the highest ranked Asian player in ATP history, moves on to the third round where he will face either American Steve Johnson or Australia's John Millman.
Nishikori won 71 percent of his first serve points and broke Kukushkin's serve four times in the 70-minute match.
"The first couple of games are the most important," he said.
In other matches Sunday, Jo-Wilfried Tsonga defeated French compatriot Vincent Millot 7-5, 6-1, Dominic Thiem beat Jozef Kovalik 7-6 (7/4), 7-6 (7/3) and Sam Querrey stopped Thiemo de Bakker 7-6 (7/5), 6-4.