The world number four needed just 67 minutes to settle a one-sided second-round encounter, running out a 6-0 6-3 winner to set up a meeting with either Julien Benneteau or Jurgen Melzer in the next round.
Murray, who enjoyed his best ever clay season last year, looked confident as he entered Court Central wearing a pair of blue headphones over his newly-shaved head, and his early play reflected his demeanour as he raced to the first set in just 27 minutes.
"It was a good start," Murray told Sky Sports 2. "Normally it's taken a few matches to get used to the clay but today I thought I moved well from the start and that is important.
"I felt comfortable and I used a lot of variety in my shots. Confidence is a big thing in tennis and I came in today feeling a lot more comfortable.
"It's a different type of game on the clay. You have to have a lot of patience. Sometimes you need to play three or four great shots to win points."
Great shots were much in evidence in a stunning first-set performance by the Scot, who broke Troicki's opening service game. A deft drop shot at the net after a period of intense defensive work secured a second break and a 3-0 lead.
Murray completed a sequence of 14 points without reply to go 40-0 up on Troicki's serve while leading 4-0, and although the Serbian recovered to deuce, Murray regrouped to break again before serving out.
A much-improved Troicki finally got on the board as he held at the start of the second set.
Murray did likewise in the next and normal service was resumed in the third when Murray broke again.
Troicki held the rest of the way to 3-4, but when Murray moved to the brink and 3-5 the cracks appeared again for the world number 30 and another break got Murray over the line.