Mercedes driver Hamilton, who trails team-mate Rosberg by 22 points in the drivers' standings, clocked a time of one minute 47.490 seconds under the floodlights at the Marina Bay circuit, completing an impressive day after he was second-fastest in FP1.
By contrast Rosberg found himself in the unfamiliar position of 13th, although the German had good reason for being over a second off Hamilton's pace, with the session halted when Lotus' Pastor Maldonado slammed into a barrier at turn 10, causing a delay.
Rosberg was on his flying lap on supersoft tyres and had just set the fastest first sector when Maldonado's accident occurred.
Subsequently the championship leader abandoned the supersofts and when he returned he was carrying extra fuel in order to simulate a race scenario, leaving him down the timesheets.
Hamilton, though, had opted to wait to use the supersofts and the decision paid dividends as he bettered the previous marker that had been set by Red Bull's Daniel Ricciardo.
By the end of the session, Ferrari's Fernando Alonso - who was quickest in FP1 - was second ahead of Ricciardo in third.
Kimi Raikkonen ended a solid day for Ferrari in fourth, while Sebastian Vettel (Red Bull) incredibly clocked the fifth-fastest time despite only entering the fray with seven minutes remaining after suffering engine trouble at the end of FP1.
McLaren pair Kevin Magnussen and Jenson Button were sixth and seventh respectively ahead of Force India's Sergio Perez in eighth, while Nico Hulkenberg (Force India) and Daniil Kvyat (Toro Rosso) rounded off the top 10.