Thompson, a two-time former champion, went 1-up at the seventh hole and never relented. She never lost the lead and closed out Miezwa on the 16th hole at Shadow Hawk Golf Club.
Thompson will meet Robin Burke, a 4 and 3 winner on Tuesday against Mary Jane Hiestand.
Medalist Kerry Postillion also posted a 2-up third-round victory on Tuesday. She knocked off Sue Romano and will battle defending champion Corey Weworski on Wednesday. Weworski advanced with a 4-and-3 win over Jamie Hoffman.
In a battle of former Women's Mid-Amateur Champions, Virginia Derby Grimes posted a 2-up win over Kathy Hartwiger.
Hartwiger missed a 3-footer for par at the 17th to fall 1-down. Grimes sank a 5-foot par putt at the last to win the hole and earn the 2-up victory.
'The match was everything I thought it would be,' said Grimes.
Grimes drew Laura Coble in the quarterfinals. Coble collected a 6-and-5 win over Ellen Dempsey.
Mary Ann Lapointe demolished Kelly Schaub, 6 and 4 and the Canadian will meet Sri Lanka's Thuhashini Selvaratnam, who defeated Shannon Ogg, 3 and 2.
Wednesday's action will feature both the quarterfinals and semifinals while the 18-hole final takes place on Thursday.