Murray, the top seed in Brisbane, will likely face Bernard Tomic in the semifinals. Tomic, for his part in making the semis, is not through yet. However, at time of writing he was closing in on a victory against Denis Istomin of Uzbekistan as the Aussie has taken the first set 6-3.
Should a "Tomic versus Murray" semifinal take place, it would feature the home country hopeful, the 19-year-old Australian Tomic, against the tournament favorite, Murray.
The Scot did not look so convincing earlier in the Brisbane tournament as he had to stage comeback victories against both Mikhail Kukushkin and Gilles Muller. Baghdatis, a former finalist at the Australian Open (2006), looked threatening pre-match. However, Murray was not to be denied.
On the other half of the draw, Alexandr Dolgopolov will face Gilles Simon in what looks like a very competitive semifinal match.
The winner of that match will face the survivor from Murray's half of the draw in the Brisbane final, a tournament that is part of the lead-up to the 2012 Australian Open.
Murray is twice a finalist from Melbourne Park, having lost in the championship match last season to Novak Djokovic and in 2010 to Roger Federer. The Scot is on the short list of favorites to win the tournament this season and will be looking for a title in Brisbane to gather confidence and momentum.