Sonego had taken out Brazilian 18-year-old Joao Fonseca in the second round and his experience proved crucial yet again as he ground out the win over American Tien on John Cain Arena.
"I don't know what to say. It's just unbelievable, I'm crazy emotional," said Sonego. "Today was so tough, I'm so sad that he had a problem. It's not the right way to win, but I'm so happy to reach the quarter-finals.
"The atmosphere was amazing, it was really special to be here. I want to do my best and I played well this week. I want to enjoy every moment."
Tien stretched his strapped right thigh after a tame double fault in his opening service game and Sonego accepted the gift of an early break to cruise through the first set.
Sonego, a singer-songwriter in his spare time with a notable presence on Spotify, hit all the right notes in the next set and looked well on his way to a comfortable win after going up 5-2 with another break before holding in the eighth game.
But Tien, who was bidding to become the youngest man to reach the quarters since a 17-year-old Goran Ivanisevic in 1989, hit back with a break in the third set, which he went on to secure when Sonego hit a forehand long.
The Italian recovered quickly, however, and hit a series of rasping forehand winners en route to a 3-0 advantage in the fourth set before sealing the victory and booking a last eight meeting with either Gael Monfils or Ben Shelton.