Murray, who now meets Switzerland's Stanislas Wawrinka, played some excellent tennis to win 6-2 6-3 6-4 in an hour and 36 minutes, which was just eight minutes more than he had needed to beat Ernests Gulbis in the previous round.
The 22-year-old Scot was a model of consistency, struck his first serve with great power and accuracy, hitting 17 aces, and bamboozled Troicki with the ingenuity of his game. In this mood he looked every inch the second favourite behind Roger Federer to win the title and end Britain's 73-year wait for a male winner here.
Murray said his performance was "very solid", although he felt he had taken time to find his rhythm in the overcast conditions. "Once I got into the match I felt much more comfortable," he said.
If the atmosphere inside Centre Court was relatively subdued it was probably because this was barely a contest. Troicki won more games than he had in his previous two matches against Murray – he took just one on the last occasion they met, in Miami three months ago – but for the most part was completely outclassed. Murray went on to win the tournament after both their previous meetings.
While Murray was making his 13th successive appearance on Centre Court, the Serb was making his first and the contrast in experience showed. Troicki looked nervous from the start, whereas Murray quickly settled into a rhythm.
At times it seemed likely that the retractable roof would have to be used for the first time. There were hailstorms, rain and thunder just a few miles down the road, but although there were drops of rain in the air at the start, it never developed into anything worse.
Troicki, 23, is at a career-high No 31 in the world rankings. Even though he has an allergy to grass, which can leave his nose and eyes streaming, and had never seen a grass court until he was 18, the Serb has the game to trouble many opponents on the surface.
The No 30 seed, attempting to reach the last 16 of a Grand Slam event for the first time, used his 6ft 4in frame to hit plenty of big serves, but Murray rarely had trouble putting the ball back into court. Most were blocked returns, which appeared to flummox Troicki. Like many of Murray's opponents, he found it hard to handle the Scot's variety, particularly when he took the pace off the ball.
Troicki started reasonably, though the early stages of Murray matches can be misleading as the world No 3 tends to play cautiously as he sizes up his opponents. Yet it was the Serb's errors rather than the Scot's winners that led to the first break of serve.
Having opened the sixth game with two successive double-faults, Troicki then put a loose forehand into the net and another long, having been forced to go for an attacking stroke as Murray cleverly pulled him forward into the middle of the court. Two games later Murray took the opening set with a second break of serve, forcing Troicki into more mistakes with forceful strokes that peppered the baseline.
Murray broke again at the start of the second set and at 3-0 had won seven games in succession. Troicki held on to maintain some respectability but never looked likely to break back as Murray fired 10 aces in the set, which ended with Troicki, under pressure, putting a volley in the net.
The pattern continued in the third set, with Murray breaking serve in the opening game after Troicki failed to pick up a lovely Murray cross-court forehand. At 2-1 down Troicki forced his lone break point of the match, only for Murray to save it with a crunching ace down the middle.
Troicki, to his credit, found some sort of form and for a moment it seemed that the weather might come to his rescue, but Murray served out for victory when he fired his 17th ace down the middle of the court.
Wawrinka, Murray's fourth-round opponent, should provide a significantly tougher test. Murray leads the 24-year-old world No 18 by 4-3 in their head-to-head record. He has won four of their last five meetings, with Wawrinka's only victory coming on clay in Rome last year.
This is the third time in a row that Murray has reached the second week here. In 2006 he lost in the fourth round to Marcos Baghdatis and in 2008, having missed 2007 with a wrist injury, he beat Richard Gasquet before losing to Rafael Nadal in straight sets in the quarter-finals. Every time he has played here Murray has gone one round better than the previous year and on the evidence of the first week you would not bet against his maintaining that record – or bettering it.
Who's next... Murray/Wawrinka head-to-head
Murray leads 4-3 (4-1 on hard courts; 0-2 on clay). First meeting on grass
Murray: 22, British, right-handed
ATP ranking: 3
ATP titles: 12
Wimbledon record: 12-3
Career record on grass: 32-8
Career record all surfaces: 198-71
Career earnings: $7,612,320
Wawrinka: 24, Swiss, right-handed
ATP ranking: 18
ATP titles: 1
Wimbledon record: 8-4
Career record on grass: 8-9
Career record all surfaces: 131-106
Career earnings: $2,860,070
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