The fourth-ranked Murray dropped the opening sets in his first two rounds as he overcame aches and pains from the offseason, but had no serious difficulty dispatching doubles partner Baghdatis in just over 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 face the winner of the quarterfinal between Bernard Tomic and Denis Istomin.
Murray saved both break points he faced against Baghdatis, the 2006 Australian Open runner-up, 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.
The Scot earned triple breakpoint two games later with a scrambling rally that included a shot between his legs that caught Baghdatis off guard, then 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 likely to link with Murray in Brisbane on the weekend to start fine-tuning 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 faced 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 was set to play Estonia's Kaia Kanepi.