New Google (GOOG) CEO Larry Page wowed Wall Street Thursday, revealing that the company’s new social network already has 10 million users and presenting his most extensive vision yet for the company’s products even as Google announced second-quarter profit jumped by 36 percent and sales increased 32 percent, handily beating expectations.

Google also notched the largest-ever quarterly increase in the size of its workforce in the second quarter, adding about 2,400 workers for a 9.3 percent jump in its head count — a figure that might typically set off alarm bells on Wall Street. But Thursday, its stronger-than-expected sales and profit numbers, particularly outside Google’s traditional strength in search advertising, clearly impressed analysts and investors.

Google’s stock had fallen nearly 20 percent this year before the June 28 launch of social network Google+, but has outperformed the market in the past two weeks. Shares jumped sharply Thursday after the company released its financial results, climbing by almost $67 a share, or 13 percent, in after-hours trading.

“This is really an outstanding quarter for revenue, and I think that reflects strength outside of their core search platform,” said Josh Olson, an analyst with Edward Jones. Revenue-generating products like mobile and display advertising and the Chrome Web browser “are really beginning to take hold and gain momentum. I think that solid sales performance really offsets some of the increased costs that we were expecting associated with their increased hiring.”

In Page’s first full quarter as CEO, Google had total revenues of $9.03 billion — its first-ever $9 billion quarter. Excluding revenue it shares with partner websites, Google reported sales of $6.92 billion and quarterly earnings per share of $8.74. Analysts polled by Thomson Reuters predicted an average adjusted earnings per share of $7.86.

Just three months ago, Page made a perfunctory appearance on the quarterly earnings call, leaving his lieutenants to explain the growth in Google’s spending and hiring. Wall Street was not impressed, and punished Google’s stock price.

But Thursday, Page was the centerpiece of the dialogue with Wall Street analysts. Google’s co-founder talked extensively about the rapid growth of Google+ and described his vision for Google’s products. He differentiated between its core search advertising franchise, its existing fast-growing consumer products like YouTube, the Android mobile operating system and Google’s Chrome Web browser; and promising newcomers like Google+ and the Google Offers discount service that launched in San Francisco and New York in recent days.

“We have substantially increased our velocity and execution this quarter — a key goal of mine since taking over as CEO” in April, Page said, in comments he also shared on Google+. “It’s why I created a new, product-focused management structure — with a clear leader responsible for each product area.”

While 2-week-old Google+ has a minute fraction of Facebook’s more than 700 million users, Page even took a thinly veiled jab at Google’s social networking nemesis, as he talked about the future potential for Google+.

“Google as a company believes in users owning their own data,” said Page. “Some of our competitors don’t believe in that. But we believe users will ultimately move to services that reflect their best interests and work well for them.”

Page told analysts he has another goal, for people to use Google products “twice a day, like their toothbrush.”

Olson said investors and analysts have been hungering for the extensive comments from the new CEO they received Thursday. In addition to sharing first-ever user statistics on Google+ — 10 million users sending and receiving 1 billion pieces of content a day — Page told analysts that Google is seeing 550,000 activations of new Android phones and tablets each day, up from 400,000 a day in May.

“I think it was significant,” Olson said of Page’s performance. “I think when you’re listening to a CEO discuss his vision, it just helps you gain confidence around his story and his strategy. I think it was something investors were looking for, and I’m glad he did it.”

Contact Mike Swift at 408-271-3648. Follow him at Twitter.com/swiftstories.