Former Olympic champion Bencic is enjoying her best run at the All England Club just over a year after giving birth.
The 28-year-old had her daughter Bella in April 2024, but has already risen back up to 35 in the world since returning from maternity leave.
Wimbledon seems to be child's play for Bencic this year, and she dispatched Andreeva in two hours and eight minutes of enthralling quarter-final action on Centre Court.
Bencic, a former world number four, will face five-time Grand Slam champion Iga Swiatek for a place in the final.
"It's crazy, it's unbelievable. It's a dream come true. I tried not to think about it at the match point. I'm just speechless," Bencic said.
"I studied all evening yesterday to come up with a plan. I think it worked out well. With two tie-breaks, it is not easy, it's just a small edge."
Bencic's only other Grand Slam last-four appearance ended in defeat at the US Open in 2019, two years before she won singles gold at the Tokyo Olympics.
She is the first Swiss woman semi-finalist at Wimbledon since Martina Hingis 27 years ago, having failed to make it past the last 16 in her previous eight visits to southwest London.
"I'm very proud. I didn't say it to myself much before, but since having Bella, I say it to myself every day. It's not only me, I wouldn't be able to do it without my amazing family and team," Bencic said.
"We worked so hard on the comeback. We are enjoying life on tour, and to play great is a bonus.
"I'm generally just really happy to be able to play again, because my body allows it."
The rising star of the WTA Tour, 18-year-old Andreeva, was the youngest women's Wimbledon quarter-finalist since Nicole Vaidisova in 2007.
Under the wing of former Wimbledon winner Conchita Martinez, the Russian had breezed through the first four rounds without dropping a set.
Andreeva said she was so focused on each point during her fourth-round tie against Emma Navarro that she did not realise when she won on match point.
But Bencic proved equally locked in, and the Swiss veteran defied a painful cracked toenail in the second set to seal her memorable triumph.
"They always crack. It is the life of a tennis player. I didn't want to take a medical time-out, so you don't have to see this," she said.
