The five-times champion, the oldest woman in the draw at 36, drew on her experience during the quarter-final to see off the Kazakh player 7-6(5) 6-2 in a brutal baseline shootout.
Williams, the 8th seed, is in her first grand slam semi since the US Open six years ago and will face Germany's fourth-seeded Angelique Kerber.
The American, who last won Wimbledon in 2008 and has since suffered health and injury problems, said lifting the trophy again would be "like that movie 'Wimbledon'".
"Real life is what Hollywood is based off of - so, hey, let's do it," she told reporters. "It's been a journey, but it's made me stronger. The good part is I always felt like I had the game. I've been blessed to have an opportunity to be here."
Williams said she and her sister Serena - the world number one, who also won her last-eight match - were not looking ahead to a possible meeting in the final.
"We are focused on the next match. We actually have to get out there and play well to win," she said. "So the talk about what could happen is not as important as what's happening in that round."
There was little to choose between Williams and Shvedova as they slugged it out in the first set, with neither finding much rhythm. But the Kazakh player's challenge crumbled after she narrowly lost a tiebreak she had led 5-2.
