Littler raced into a 4-0 lead before dropping his first set of the match, but would quickly atone and go on to win the quarter-final clash.
He averaged 101.93 on his way to the final four, hitting five 180s as he cruised past Dolan.
The 16-year-old is the youngest player in history to win a match at the PDC World Championship, and to reach this stage of the tournament.
Following the win, the teenager will at the very least be guaranteed a place in the top 64 of the rankings at the end of the World Championships.
He will face Rob Cross in the semi-finals, who produced an incredible comeback victory against Chris Dobey earlier in the day.
Speaking to Sky Sports following the match, Littler admitted it was hard to process his victory.
"Wow, I'm in a semi-final on my debut," the teenager said.
"I've earned it, I just threw another ton-plus average there. It's going well."
Littler was also clear on his chances of winning the trophy, as well as his confidence in his own skills.
"If I keep it up I've got a good chance!
"Now I am dreaming, I'm two games away so I'm thinking about lifting the title.
"My board management is one of the best, I know what I'm going for and I know what to set up."
