Baghdatis, the No. 6 seed, got by the fourth-seeded Dodig 6-4, 7-5. Baghdatis lost his serve just once. That came in the 10th game of the second set when Dodig pulled even at 5-5.
But Baghdatis answered with a break of his own and then served out the match.
No. 3-seeded Mikhail Youzhny survived a 2-hour, 42-minute battle against eighth-seeded Ivo Karlovic, winning 7-6 (12-10), 3-6, 7-6 (8-6). Karlovic had 22 aces and won 77 percent of the points on serve but Youzhny squeaked through with the tiebreaker wins.
Lukas Lacko posted his second straight upset, knocking off seventh-seeded Robin Haase 6-4, 6-4 behind three breaks. He beat No. 2-seeded Alex Bogomolov Jr. in the second round.
Michael Berrer topped Jurgen Melzer 5-7, 6-4, 6-4 in the other quarterfinal. He faced just one break point over the last two sets.
Youzhny goes against Berrer, who won their lone previous meeting in 2007, in one semifinal while Lacko draws Baghdatis in the other. Lacko was a four-set winner over Baghdatis last year at Wimbledon in their only career meeting.
Celebrity Families of 2014 [PHOTOS]