Becker defeated the third-seeded title-holder 7-6, 6-3 to record his fourth consecutive victory over his compatriot. His steady serve-and-volley game on the fast surface in the Globe Arena evoked memories of his best form.
'Frankly, I'm not far away from the form I had when I was No 1 in 1991,' said Becker, currently ranked sixth in the world. 'I'm stronger and in many ways better, but I'm not able to produce top matches every week.'
Becker has won three ATP titles this year but this has been punctuated by six first-round defeats. The three-times Wimbledon champion's last Grand Slam title, the Australian Open, was three years ago.
Stich, who beat Goran Ivanisevic in the final here last year, is now in danger of failing to qualify for the end of season ATP finals in Frankfurt, where he is the reigning champion.
'I'm still in seventh or eighth place and the others will have to do better than me in the next two weeks to beat me to Frankfurt,' said Stich, who will play in both Paris and Antwerp to try to guarantee himself a place in the finals.
In the Stockholm semi-finals, Becker, who has won the tournament three times, will now face the world No 1, Pete Sampras, of the United States, who beat the only remaining Swede, Magnus Larsson, 6-1 6-4. Sampras's coach, Tim Gullikson, was recovering in his hotel room after fainting and falling on to a glass coffee table. He was treated in hospital for cuts and a broken nose.Reuse content