Meanwhile, manager Simon Grayson praised Alan Gow for salvaging a point against the Bluebirds with an injury-time equaliser.
The former Oldham trainee has made 139 appearances for Simon Grayson's side since joining from Norwich in August 2007.
Fox, 25, was signed by Simon Grayson in January 2006 for Blackpool after over two years on the Old Trafford books.
The result will be a huge relief to Simon Grayson's side, who were comprehensibly beaten in their opening league match at Southampton on Saturday.
Blackpool boss Simon Grayson was also left celebrating after his side secured the Championship status, having been promoted from League One 12 months ago.
Joe Royle, Peter Reid, Graeme Souness and Jean Tigana had already been interviewed for the position, while Paul Jewell, Iain Dowie and Simon Grayson were also linked.
United's manager Simon Grayson was marking three years in charge of the Elland Road club on Boxing Day but his side struggled to make it a happy celebration.
Leeds manager Simon Grayson angrily invaded the field of play but replays suggested Cohen won the ball cleanly and he can be regarded as unfortunate to have been sent from the field.
Prior to Sunday Blackpool had won their last seven games of the season scoring 22 goals in the process, but Simon Grayson's side found Oldham an altogether tougher proposition in the first half.
Leeds began the last decade at the top of the Premier League and challenging in Europe until a financial meltdown saw them slip down the divisions, but the current side under manager Simon Grayson are restoring pride to a once great club who were winning at Old Trafford for the first time since 1981.
"Just a few years ago, these countries were untouchables, " says Simon Mandel, who follows Central and Eastern European countries for Auerbach Grayson, a New York broker-dealer that specializes in emerging and frontier markets.
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