Troicki, ranked 31st in the world, overcame Nadal 6-3 7-6(3) in an hour and 34 minutes to secure his first ever victory in five previous attempts against the 14-time grand slam winner.
The unseeded Serb broke twice to seal the opening set before Nadal came back strongly in the second. The Spaniard saved a match point at 5-4 down but was defeated in the tiebreak.
"I played really well," Troicki said. "I was aggressive, I served well, I hit the ball nice. It was a great feeling on the court playing like this... against Rafa Nadal, who is a great champion."
Twice Shanghai Masters champion Murray, who claimed the China Open title last week, had no such trouble as he won 6-3 6-2 as he won 70 percent of second-serve return points.
The second-seeded Briton, who scraped through a testing encounter with Johnson at the Rio Olympics in August, also saved the one break point he faced in the first set.
He will play Frenchman Lucas Pouille in the third round.
"I felt like I was creating a lot of chances on his serve. I thought I moved well for the first match in new conditions," Murray told reporters.
"I was timing the ball well. I felt like I was controlling a lot of the rallies. Yeah, for a first match after playing pretty different conditions a few days ago, it was good."
Australia's Nick Kyrgios lost to Germany's Mischa Zverev 6-3 6-1 with another controversial display in which he appeared uninterested throughout, landing a series of half-hearted serves and barely moving to meet his opponent's returns.
The 21-year-old also clashed with spectators before being booed off the court after a match that lasted just 48 minutes. Kyrgios, later apologised on his Twitter account, saying his performance was "not good enough". [L4N1CI3OH]
Seventh seed Tomas Berdych lost to Marcel Granollers of Spain 7-6(4) 7-6(1), while third seed Stan Wawrinka, the U.S. Open Champion, beat Britain's Kyle Edmund 6-3 6-4 and Canada's Vasek Pospisil battled past Grigor Dimitrov 7-5 7-6(2).
(Reporting by Ian Rodricks in Bengaluru; Editing by Ken Ferris)
