Lee was busy for only 81 minutes on the way to booking a meeting with the winner of the match between the red-hot title favourite, Stephen Hendry, and Dave Harold.
"I knew it was important not to let him settle down," Lee said, who was always in command after sailing through the opening frame with a run of 79.
Lee, who also appeared in the last four of the Liverpool Victoria UK Championship and Regal Scottish Open last season, added the second frame on the blue and moved 3-0 ahead with breaks of 38 and 47.
By now Hann was getting impatient and when he took on and missed an ill- advised long blue after clumsily running out of position in the fourth frame, his frustration was evident.
"That's when I knew I had him," the 24-year-old from Trowbridge said. "I'm not so sure about his [Hann's] temperament," he added. "Quinten was giving me the look all match, but all I could see was six pockets and the balls."Reuse content