Van Gerwen won the title in 2014 and 2017 and looked every inch the top seed in a brilliant performance against Anderson, who in contrast struggled to find his best form.
— PDC Darts (@OfficialPDC) December 30, 2018
Anderson at least avoided a whitewash by winning the sixth set, but that was where his resistance ended.
Not surprisingly, Van Gerwen was thrilled with his performance, telling Sky Sports: "I think I played really well, especially early doors. Gary couldn't find his form in the beginning and I took advantage of that. I didn't give him any time to breathe in this game. After the 5-0 I was getting confident."
Both Smith and Aspinall were playing in the last four for the first time, but 10th seed Smith had the pedigree against debutant Aspinall and made it count.
Smith made a tremendous start and took a 2-0 lead, but Aspinall fought back to level at 2-2 and then again for 3-3.
But Smith was relentless in his scoring and clinched victory at the first attempt with a 121 checkout.
The 28-year-old averaged 105.22, hit 17 180s – an individual record in a World Championship semi-final – and had a checkout percentage of 51.11.
An emotional Smith said: "I've never felt like that ever. I'm so happy, I don't know what to say. I just took my chances when they came.
"I nearly made a mess of myself tonight, it felt like I was going to give birth to an ostrich egg or something. I was so nervous but I'm so happy I held it together. I'm one step away from living my dream."
Aspinall had no regrets at the end of his brilliant run, saying: "I've enjoyed every single minute of it. I never thought I'd get to the semi-final.
"It wasn't my night but I'm so happy to be involved in a quality game. I wish Michael all the luck in the world because he deserves to win this."
Smith has won only four of his previous 25 meetings with Van Gerwen, and the Dutchman said: "It's going to be a phenomenal game, but I'm going to be a bit different to Nathan Aspinall.
"This means the world to me. I do a lot to come to this stage but the work is not done yet, I have to do more."