The case, which accuses Google of breaking various laws regarding fair dealing with consumers, can go forward, Judge Ronald Whyte ruled late on Monday in the U.S. district court in San Jose.
He denied Google's motion to dismiss portions of the case that alleged its advertisements were "unfair, deceptive or misleading." He also denied motions to dismiss allegations that Google breached the "duty of good faith and fair dealing."
Whyte dismissed other parts of the lawsuit, but said he would allow them to be refiled if they are amended.
Google had asked the judge to dismiss the case entirely.
In the lawsuit, the parent said she had created a Google Play account for her Samsung Galaxy tablet and connected it to her debit card. She then used her password to download and pay for a 99-cent game known as "Marvel Run Jump Smash."
But her password remained open for 30 minutes after the download and during that time, her child, whose age was not disclosed, racked up $65.95 in purchases within apps, the lawsuit said.
The Federal Trade Commission settled a similar case with Apple Inc in January and filed a lawsuit against Amazon.com in July related to allegations that children sometimes accumulated hundreds or even thousands of dollars in charges that parents did not authorize because of inadequate controls put in place by the companies.
The FTC has not said if it is investigating Google for similar practices.