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Call it Kinectification. Microsoft said today that its video-game business grew dramatically thanks to sales of its Kinect motion-sensing system.

The Entertainment & Devices division — which includes Xbox 360 and PC games, Zune, Windows Phone 7, and consumer software — generated $3.7 billion in revenue in the quarter ended Dec. 31, up 55 percent from $2.4 billion a year earlier.

Peter Klein, chief financial officer, said in a conference call that Kinect is the “fastest-selling consumer electronics device in history.”

That shows that, after many years of skepticism and losses, Microsoft’s game business has hit its stride. Kinect has given the company a much-needed boost in sales at a time when Microsoft might normally have had to introduce a new game console. The Xbox 360 was introduced in 2005. If it were a normal console cycle, Microsoft would have to introduce a new box this year. But Kinect let the company postpone the new console and keep gamers entertained with something new.

Operating income for the Entertainment & Devices division was $679 million, up from $365 million a year ago. Microsoft saw 42 percent growth in U.S. console sales in 2010, mainly because it introduced a slimmed-down version of the Xbox 360 in June. Kinect also drove new game software and console sales as well.

Microsoft sold 6.3 million XBox 360 consoles during the holiday season, up 21 percent from a year ago. The company sold 8 millon Kinect sensors  in the first 60 days after launch. Memberships of its premium XBox Live online service grew 30 percent to above 30 million active members in the second quarter of its 2011 fiscal year, according to the company. Microsoft is expecting 50 percent growth in its entertainment division in the third quarter, and 40 percent overall for its 2011 fiscal year.

Microsoft said Windows Phone 7 is available on 9 smartphones launched by 60 operators in 30 markets.

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