The Facebook obsession has already led to Google's creation of its own social network, Google Plus, and inspired changes in Google's privacy practices and Internet search results. Those changes have raised questions about whether the Internet's most powerful company has forsaken its "Don't Be Evil" motto in its zeal to protect its online advertising empire.
"Facebook awoke Google to its shortcomings in the social aspect of the Internet. It wasn't something that could be ignored," said Steven Levy, whose book "In The Plex" provided an inside look at Google's origins and evolution over 14 years.
Fretting about Facebook may seem like overkill, given Google's dominance of the Internet's lucrative search and advertising market. Last year, Google's sold $36.5 billion in advertising – 10 times more than Facebook's $3.2 billion.
But Page realized Facebook has been carving out a competitive advantage that could be leveraged to topple Google.
Since its 2004 inception, Facebook has been stockpiling valuable information about people's social circles and interests. The volume of insightful data pouring into Facebook has mushroomed along with its service's popularity. That has provided Facebook with the means to target ads more precisely and deliver content tied to a user's hobbies and tastes.
Google couldn't use most of that data to refine its search engine and other products, which is why it developed its own social network.
Since its debut nine months ago, Google Plus has attracted more than 100 million users. Although it lags Facebook's 845 million, the number is far greater than Facebook's tally at that stage in its history.
But Google Plus hasn't proven it can hold users' attention. Visitors have been spending an average of just a few minutes per month on Google Plus compared with six to seven hours on Facebook, according to the research firm comScore .
Nevertheless, Google Plus and other social networking features introduced since Page took over allow the company to learn more about its users' lives, just as Facebook has done for years on its online hangout. Now, Google can try to use some of that knowledge to sell more ads, the source of virtually all its revenue.
Facebook's threat figures to become even greater after the company emerges from an initial public offering of stock, likely to be completed next month. The IPO is expected to raise $5 billion and generate free publicity that could attract even more traffic to Facebook. The IPO will likely eclipse Google's 2004 stock market debut as the biggest for a U.S. Internet company.
Google said Page was too busy for interviews about his past year as CEO, a role he reclaimed after surrendering the helm to Schmidt in 2001. Page had been CEO during the company's first three years, but early investors demanded a more experienced leader.
Schmidt, now Google's executive chairman, last year described his failure to mount a more serious challenge to Facebook as one of his biggest blunders.
When he took over as CEO, Page quickly made his top priority clear by moving Google's executive offices into the same building as the team working on Google Plus.
Page also tied a portion of employee bonuses to the success of Google Plus and eliminated what he considered to be unnecessary distractions by closing more than 20 of the company's less popular services, including an initiative to digitize health records.
"Larry is driven by his paranoia about Facebook. Clearly, these are two companies at war with each other," said Ken Auletta, who got to know Page while writing his book about the company, "Googled: The End of the World As We Know It."
Page already has plenty of other challenges to confront as he enters the second year of his reign.
Google is also grappling with broad regulatory investigations in the U.S. and Europe into its business and privacy practices. Its Android operating system for smartphones and tablet computers is clashing with Apple Inc. in the increasingly important mobile computing market. And it is close to completing its biggest acquisition ever – a $12.5 billion purchase of cellphone and tablet computer maker Motorola Mobility Holdings, pending approval from the Chinese government after winning clearances elsewhere.
Page also is trying to win over Wall Street.
Although Google is more prosperous than ever, its stock price hasn't kept pace with the rest of the technology sector. Some investors have been turned off by Google's rising expenses under Page. Others were alarmed by a drop in the prices paid for Google's search-driven ads late last year. The company's stock price has climbed by 9 percent since Page became CEO, but that trailed a 12 percent gain in the technology-laden Nasdaq composite index. The broader S&P 500 index, which includes Google, has increased by 6 percent over the same period.
Some of Google's tactics to fend off Facebook have been interpreted as signs that Google is turning into a ruthless company willing to go to any length to protect its core business.
That's something Page and co-founder Sergey Brin vowed would never happen when Google filed its plans to go public in 2004. In a letter to investors, Page expounded on the reasons Google adopted "Don't Be Evil" as one its guiding principles. "We believe strongly that in the long term, we will be better served ... by a company that does good things for the world even if we forego some short-term gains," Page wrote.
The sincerity of those commitments is being questioned as Google digs deeper for personal data.
Another privacy backlash grew out of research a Stanford graduate student published in February. It showed that the company had been bypassing the security settings in Apple's Safari browser for iPhones and iPads to track Web surfers' online activities. Google called the intrusion an inadvertent offshoot of an effort to enable Safari users to press Google Plus's version of Facebook's "Like" button. Google disabled the tracking after it was revealed.
Google also tweaked its search results in January to give users the option to highlight results from Google Plus. Among other things, the search engine began to include suggestions on people to follow on Google Plus while excluding recommendations for Facebook and Twitter's messaging service, both of which are used more widely than Google Plus. Google says its search engine can't pull enough information from Facebook and Twitter to provide the same recommendations as it does for Google Plus.
Critics, though, scoff at that explanation and point to the bias as another example of how Google is abusing its dominance of Internet search to steer more traffic toward its own services. Those complaints are a central part of the regulatory investigations under way in the U.S. and Europe.
Both Auletta and Levy view what's been happening at Google as part of the inevitable maturation of the company and Page, who turned 39 last week.
"That idealistic flame still burns in Google," Auletta said. "But what happens, as time goes on, and you are no longer a young company, you have to make the compromises of adulthood...Facebook eventually is going to have to face a lot of the same questions."