Murray got off to a quick start as he took a 4-0 lead in the first set, eventually closing it out 6-2.
There were no breaks in the second set until the 5th game, when the world no.4 broke Baghdatis’ serve and from then onwards didn’t let the match out of his hands.
“I played very well. I moved very well from the start – which wasn’t the case in my first two matches – so I’m really, really happy,” said Murray after the match.
He and Baghdatis played doubles together, but went out in the quarterfinals.
Murray’s next opponent will be Australian Bernard Tomic, who defeated Denis Istomin of Uzbekistan 6-3 7-6 (4).