Baghdatis, from Cyprus, followed a second-round win over sixth-seeded Viktor Troicki with a come-from-behind 4-6, 6-2, 6-3 win over No. 4-seeded Australian Lleyton Hewitt. Hewitt was the only seeded player to reach the tournament quarterfinals.
Baghdatis played a solid match, getting into only two break-point situations -- losing both -- in the two-hour match. Hewitt suffered four service breaks, including three in the second set when Baghdatis established control.
In other quarterfinals Thursday, Frenchman Richard Gasquet stopped Italian Potito Starace 6-3, 7-6 (9-7); France's Julien Benneteau defeated Argentine Leonardo Mayer 6-4, 6-7 (5-7), 6-0; and American Mardy Fish was a 7-6 (7-5), 6-2 winner over Australian Peter Luczak.
Fish will play Baghdatis in Friday's semifinals. Baghdatis is 2-0 against Fish, including a 7-5, 7-5 win last week. Benneteau and Gasquet, the other semifinal pairing, have met once before with Gasquet winning 6-1, 6-4 in the 2007 Australian Open.
Saturday's title match will be worth $67,260 to the champion.
Notable deaths of 2014 [PHOTOS]