The 21-year-old Bulgarian, ranked 72 in the world, has never won a tour title and set up a semi-final clash against Argentina's David Nalbandian by beating South Africa's world number 30 Anderson 4-6 6-4 6-3.
"I got couple of tears," Dimitrov said. "It was a good moment. I always wanted to share this with the people that I love so I was glad because my father was there, and I think it was a big moment for him mainly."
With the top seeds Andy Murray and Jo-Wilfried Tsonga already out and number three Janko Tipsarevic joining them earlier on Friday after losing a third-round encounter to Lu Yen-Hsun, it was left to the lesser lights to entertain on the West London grass.
Marin Cilic moved into the semi-finals when his opponent Lu, playing his second game of the day after rain delays, retired hurt midway through the second set.
Cilic will play Sam Querrey, Queen's champion in 2010, who beat Croatia's Ivan Dodig 7-5 3-6 6-3.
Nalbandian also appeared twice, first winning his third round against Edouard Roger-Vasselin and then edging past Xavier Malisse 4-6 7-6 6-4.