Nadal advanced past Israeli Dudi Sela 6-3 6-4, taking the critical second-set break in the seventh game, while Nishikori cut down South African Kevin Anderson 6-4 6-3.
Third seed Raonic has been sidelined by a right leg injury that forced him to concede a walkover in the Delray Beach Open final last month and to withdraw from the Mexican Open and BNP Paribas Open.
“I have to be very happy with just the outcome, that I was able to get the win today, that I have another chance to play in two days,” said the world number five.
Raonic breezed through the opening set and led 3-1 in the second before Serbia's Troicki battled back.
World number 38 Troicki, who has reached the fourth round in Miami twice, drew level at 5-5 before Raonic’s pressure helped him secure the deciding break.
Raonic advanced to play American Jared Donaldson, a 6-4 6-4 winner against 28th seed Mischa Zverev of Germany.
Raonic said he has been helped by the addition of former world number 69 Jesse Levine to his coaching support.
“He's somebody that I get along with great, is a little bit closer to my age as well, and somebody that I can play with on court and put in hard hours with,” he added.
A string of upsets unfolded later in the day with world number 13 Grigor Dimitrov eliminated in straight sets by Argentinean Guido Pella 6-3 7-6(4).
Dimitrov, who lost to Nadal in the Australian Open semi-final, has now lost three of his last six matches since winning the Sofia Open last month.
American Donald Young knocked out 11th seed Lucas Pouille 6-2 6-4, Federico Delbonis took down 15th seed Pablo Carreno 1-6 7-5 6-2, while Frenchman Gilles Simon fell to German Jan-Lennard Struff 6-1 6-1.
In earlier action, Frenchman Jeremy Chardy defeated seventh-seeded former U.S. Open champion Marin Cilic of Croatia for the first time since 2009 to move into the third round with a 6-4 2-6 6-3 win.
(Reporting by Larry Fine and Jahmal Corner; Editing by Andrew Both and Peter Rutherford)
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