The 37-year-old cruised to a comfortable 10-2 win against his compatriot earlier today to set up a meeting with Ronnie O'Sullivan at The Crucible.
"It was most unexpected really - I don't think I've beaten him since 2003," he told BBC Sport. "But I didn't say that to him, I was just trying to keep it out of my head. I felt comfortable out there, to beat Mark even 10-9 would be difficult. So to win 10-2 is beyond my wildest dreams really.
"It's not nice, we have grown up with each other since we were young. We are like brothers. It is hard but we are both professionals and luckily for me it was my turn to win."
Stevens has previously finished as runner-up at the World Championship in 2000 and 2005.