She’s earned the No. 1 spot in our annual ranking of the Most Powerful Women in Business. But to keep Big Blue growing, Rometty will have to sell IBM like never before.

By Jessi Hempel, senior writer

FORTUNE — Ginni Rometty’s first customer conference as CEO of IBM (IBM) was an unusual affair, especially by Big Blue’s buttoned-up standards. The June confab took place in an airy loft in Manhattan’s hip Chelsea neighborhood. When the tiny elevator arrived to whisk a group of us to the meeting space, the doors opened and there was Rometty, flanked by a couple of visibly nervous assistants. "Really good to see you!" she said, clasping my hand warmly as her handlers checked their watches. The presentation was about to begin and Rometty still wasn’t wearing her microphone. "Isn’t this neat?" she asked.

The program started late. At 5-foot-11, with blond hair tucked behind a headband, Rometty, 55, has an almost regal bearing, but on this day she flubbed her entrance, bounding onto the stage before she could be introduced. She laughed it off. When an audience member’s ringing cellphone interrupted the events, she joked, "I hope that isn’t mine!"

You wouldn’t catch Lou Gerstner or Sam Palmisano trying to smooth over someone else’s faux pas. Rometty’s two predecessors also are unlikely to have hosted a sales meeting in a loft, and they definitely wouldn’t have described the proceedings as "neat." But they surely would have approved of Rometty’s agenda that June day. She had assembled some familiar faces, the chief information officers who buy billions of dollars of software, tech services, and hardware from IBM (No. 19 on the Fortune 500), but she had also invited their chief marketing officers. (Thus the trendy venue.) Her ambitious — and yes, unusual — plan: Get the marketers to use IBM tools to sort their data for nuggets that will help them better reach customers and sell more stuff.

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When Rometty (pronounced RAH-metty) became IBM’s ninth CEO — and its first woman chief executive — she took control of the 19th-largest company in the world by revenue (2011 sales surpassed $107 billion) and, at presstime, the fifth largest by valuation, with a market cap of $235 billion. Her influence on the world of technology and her company’s impact on the financial markets earn her the No. 1 spot in Fortune’s annual ranking of the Most Powerful Women in Business. She inherits a company with an enviable growth record for its enormous size. Over the past decade, the company has increased profits by an average 16% every year, returning 12% annually to shareholders.

She also needs to live up to almost ridiculously high expectations: IBM has said it will add $20 billion more in revenue growth in the next three years. To put that in perspective, that’s a business roughly the size of Nike (NKE), No. 136 on the Fortune 500.

Not that any of this is a surprise to Rometty, a 31-year veteran of IBM who is known to have thick binders of background material and data prepared for her in advance of meetings. Indeed, the most surprising thing about her June customer debut was how loose and improvisational it was. She’s not a stiff — "There’s nothing imperious or imperial about her," notes Harvard Business School’s Rosabeth Moss Kanter — but Rometty rarely leaves anything to chance. For example, she declined to be interviewed in person for this article, and would answer questions only via e-mail.

Rometty was at Palmisano’s side for much of his decade-long tenure, and became a serious candidate to succeed him about four years ago. And she was personally involved in setting the high bar that she must now clear. She and other senior leaders helped him develop the five-year plan — dubbed "2015 Roadmap" — that has IBM targeting more than $125 billion in revenue that year.

For Rometty the challenge of meeting that goal is only partly about inventing new technologies to sell to her existing clients. Growth at IBM’s scale also means creating new markets, much the way it did with its Smarter Planet campaign, which sold nontechies such as mayors and police chiefs on the idea of using software to monitor and manage traffic, water systems, and sanitation trucks. Now Rometty is making a similar pitch to marketing executives, promising that technology will change the way they do their jobs. It won’t be an easy sell: Marketers are less apt than bureaucrats to be wowed by a charismatic CEO or statistics about petabytes. Many are accustomed to seeing computing as a tool to support their creative endeavors, not the starting point.