The No. 4-ranked Murray dropped the opening sets in his first two rounds here as he overcame soreness and stiffness from the offseason, but had no serious difficulty dispatching doubles partner Baghdatis in little more than an hour.
Murray, who has lost the last two Australian Open finals and has recently hired Ivan Lendl to help him break his Grand Slam title drought, will next play eighth-seeded Bernard Tomic.
The Australian teenager, a quarterfinalist at Wimbledon last year, converted the only breakpoint chance of the match to beat Uzbekistan’s Dennis Istomin 6-3, 7-6 (4).
Murray saved both break points he faced against Baghdatis, the 2006 Australian Open runnerup, and converted all four of his own.
After a difficult service game to hold in the fourth game of the second set, Murray broke in the fifth to take a 3-2 lead.
He earned triple breakpoint two games later after a scrambling rally which included a shot between his legs that caught Baghdatis off guard and secured a 5-2 lead on the next point when he successfully challenged a baseline call.
“I played very well today ... moved very well from the start, which wasn’t the case in the last two matches, so really, really happy,” Murray said. “The aches and pains I had from the first two matches have gone, so it’s good.”
Murray has lost three major finals, and is still desperate to end a drought for British men in Grand Slam singles that dates back to 1936. Lendl, an eight-time Grand Slam titlist, arrived in Australia from the United States on Friday and was due to meet up with Murray in Brisbane on Saturday to start finetuning for the Australian Open, which starts Jan. 16 in Melbourne.
“The Australian Open has always been the tournament that I’ve done my best at since I was young,” Murray said, “So I look forward to going back there and hopefully go one better than last year.”
In women’s semifinals, Australian Open champion Kim Clijsters was playing Daniela Hantuchova, who got a walkover in the quarterfinals when 13-time Grand Slam winner Serena Williams withdrew from the tournament after injuring her left ankle, and Francesca Schiavone is against Estonia’s Kaia Kanepi.
