IBM has surpassed Microsoft in market worth, an ironic turn of events considering that Microsoft outsmarted IBM years ago and left the company practically for dead. It’s a sign of how Microsoft hasn’t been able to adequately adjust to a changing world. Microsoft would do well to examine how IBM turned around its fortunes, and learn some lessons from the company’s revival.

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Bloomberg reports that as of the close of the market yesterday IBM had a market value of $214 billion, surpassing Microsoft’s $213.2 billion. It was the first time since 1996 that at the close of a trading day IBM had a greater market value than Microsoft, Bloomberg says. Apple, meanwhile, had a market value of $362.1 billion as of yesterday, Bloomberg calculates.

Decades ago, the tiny upstart Microsoft outsmarted the computing beheamoth IBM when Microsoft bought the rights to a clone of Digital Research’s 86-DOS operating system, tweaked it and renamed it MS-DOS, as part of a deal with IBM to provide the operating system for the new IBM PC. Microsoft got a significant amount of money from the deal, and still retained the rights to DOS, leading the way to a flood of clones that eventually swamped IBM.

When Microsoft thrived and IBM stumbled, it was seen as symbolic of the rise of the personal computer and the decline of mainframes. Microsoft was the future; IBM the past.

IBM, though, eventually recast itself, getting out of the PC business entirely by selling off its PC division to Lenovo. And it focused instead on software and services. It was a prescient move, not only because of the great demand for software and services, and the high margins there, but because even though no one noticed, the PC itself will eventually be surpassed by other devices such as smartphone and tablets, and demand for it further hurt by the growth of the cloud.

So what can Microsoft learn from IBM? That sometimes you have to ignore your own company history and culture, and set a very different direction. IBM became immensely successful because of hardware, but after its decline it became immensely successful because of its focus on software and services.

What’s the equivalent for Microsoft? To end its heavy reliance on Windows to prop up the company. Windows will remain a cash cow, but PCs don’t lead the way towards growth. If the company wants to grow, it needs to better target mobile devices and the Internet, and not necessarily view the world through Windows. It’s not clear that will happen. At the 2011 Microsoft Worldwide Partner Conference (WPC 2011) in July, CEO Steve Balmer made it clear in his opening speech that he believes that Microsoft’s future is Windows, saying:

“Windows is the backbone product of Microsoft. Windows PCs, Windows Phones, Windows slates. Windows Windows Windows Windows Windows.”

I don’t believe that’s the way to the future, though, and there’s evidence that Ballmer might not believe that either. In August Microsoft laid out in a blog its vision about the future of TV, entertainment and the living room. Windows wasn’t in that vision. Instead Microsoft sees the Xbox 360, Kinect, and Bing teaming up to transform entertainment-related technology.

That willingness to abandon what’s worked in the past is what saved IBM. If Microsoft does the same, it can help the company regain its position as the pre-eminent tech giant.