Sabalenka was the firm favourite to reach the semi-finals of a Grand Slam she is yet to win but was frustrated by 37-year-old veteran Siegemund.
It was the unseeded German, currently ranked No. 107 in the world, who took the first set 6-3 after getting a double break on big-serving Sabalenka.
The world number one forced a third and final set by claiming the second 6-2 but continued to find Siegemund a tricky customer.
Siegemund clinched an early break in the deciding set and Sabalenka let her emotions get the better of her after failing to break straight back.
After guiding a forehand wide, the 27-year-old smashed the net with her racket, leading to loud boos around Centre Court.
Former British number one Annabel Croft said on BBC Radio 5 Live as cited by Sports Central: ‘Sabalenka is entering into dangerous territory now. ‘In the past when she has been up against the wall, she is usually like Serena [Williams] where she galvanises and brings it all together. I am not totally convinced that is going to happen in this match.’
It was not the only angry outburst from Sabalenka, who threatened to smash several balls into the crowd after being broken before composing herself in the nick of time.
Sabalenka was frustrated not only by Siegemund’s superb tennis but also the German’s antics as a notoriously slow player.
She received a time violation from the umpire during the third set which former British number one Sam Smith admitted ‘had been coming’.
She said: ‘The umpire has been very generous out here. ‘He is hugely experienced and he had been letting it go. ‘It is not the first time Siegemund has had a time violation at this year’s championships.’
A final-set tie-break beckoned but Sabalenka got the decisive break to finally break the resolve of Siegemund, who enjoyed her best ever run at the All England Club.
Sabalenka, a three-time Grand Slam winner, will face Amanda Anisimova or Anastasia Pavlyuchenkova for a place in the Wimbledon final.
Reacting to Sabalenka’s comeback win, Croft added: ‘What a match! What an absolutely enthralling contest that was. ‘I reckon that is one of the most uncomfortable, most painful matches Sabalenka has ever had to play in her life. ‘Siegemund played that match so well tactically to make her play some of the worst tennis of her career.’
Sabalenka, meanwhile, said: ‘That was a real test. I need some time to cool down and recover after this. ‘She pushed me so much. After the first set I was looking at my box and thinking, “book the tickets, we are about to leave this beautiful place”. ‘She played an incredible tournament and match. I’m just super happy with the match and win.’
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