* Serena recaptures world number one ranking
* American faces Sharapova in semi-finals
* Radwanska sets up last four clash with Azarenka (Updates with Radwanska victory)
DOHA, Feb 15 (Reuters) - Serena Williams showed tennis was not just the domain of teenagers as she climbed back to the top of the world rankings on Friday, becoming the oldest female to hold the coveted position at the age of 31.
The American is world number one for the sixth time in her storied career after finishing off former Wimbledon champion Petra Kvitova 3-6 6-3 7-5 with a thumping ace in the quarter-finals of the Qatar Open.
Williams will meet Russian Maria Sharapova, who had also been in hot pursuit of the number one ranking this week, in a lip-smacking semi-final on Saturday.
"I'm so sensitive nowadays, I'm always crying! I've just been through so much and never thought I'd be here again," Williams, who recovered from 4-1 down in the third set, told the crowd as she fought back tears.
At 31 years, four months and 24 days, she will be the oldest woman in the top spot since computer rankings began in 1975. Williams eclipses fellow American Chris Evert, who was 30 years, 11 months and three days when she last held the ranking in 1985.
Since then teenagers like Steffi Graf, Monica Seles and Sharapova have often been world number one but, more than a decade after first claiming top spot, 15-times grand slam champion Williams showed she still hungers for success.
It was little wonder the second seed was so emotional after all the injuries, illnesses and surgery she has endured since last relinquishing the number one spot in October 2010.
While Williams relishes the prospect of beginning her 124th non-consecutive week as the world's best female player when the new rankings are officially unveiled on Monday, Sharapova must take consolation from continuing to progress at the Qatar Open.
The Russian brushed aside Australia's Samantha Stosur 6-2 6-4 on Friday having not dropped a set in her three matches, a feat equalled by outgoing world number one Victoria Azarenka of Belarus who saw off Italian Sara Errani 6-2 6-2.
Third seed Sharapova, who held an 11-2 career record over Stosur going into the match, was never threatened in her 82-minute victory.
Top seed Azarenka will face Agnieszka Radwanska in the semi-finals after the fourth seed overcame former world number one Caroline Wozniacki of Denmark 6-2 7-5 in the late match. (Reporting by Pritha Sarkar and Martyn Herman in London, editing by Tony Jimenez and Ken Ferris)