The Scot, who reached the last four at the tournament last year, broke serve in the first game and never looked back, wrapping up a straightforward victory after 67 minutes when Troicki sent a backhand wide.
"It was very good, getting off to a good start in the match," Murray told a news conference.
"Sometimes it's close, tight, first set, first match on clay, kind of anything can happen. You can start rushing. It's very easy on the clay to start rushing and making mistakes but because I got ahead I didn't need to do that."
Third seed Murray, who received a first-round bye, looked in fine form as he unsettled Troicki with some exquisite drop shots and stuck to his usual tough defence to deny his opponent any chance to come back.
"I moved well. I was sliding pretty well on the court. Normally that's the thing that takes time to get used to... For me that's a good sign on the clay, whether I'm playing well or not," the Scot said.
Troicki took only five points on Murray's serve and never threatened the Scot, who will take on either France's Julien Benneteau or Austrian 15th seed Juergen Melzer for a place in the quarter-finals.
Spaniard Fernando Verdasco, the 13th seed, recovered from a set down to move past Croatia's Ivan Dodig 3-6 6-3 6-1 and set up a third-round clash with Frenchman Jo-Wilfried Tsonga, the fourth seed.
Tsonga pleased the crowd, who sang in celebration of his 27th birthday after he defeated German Philipp Kohlschreiber 6-2 6-4.
German Florian Mayer, the 14th seed, made a first-round exit after a 3-6 6-1 6-3 defeat to Kazakhstani qualifier Mikhail Kukushkin.