Hamilton has already secured the Formula One title but Rosberg has won the past two races and will target a sixth straight pole position in Saturday's qualifying.
Rosberg's best lap was 0.138 seconds faster than Hamilton at the Yas Marina circuit, although he believed the British driver eased off during his flying laps on the softer tire Friday.
"Lewis didn't show his pace on one lap," Rosberg said. "It's clear that he still has some in reserve. Today is not the real picture."
Hamilton had complained during the first practice session about the handling of the car, and although some adjustments improved its performance in the evening session, he believed there was room for further improvement ahead of qualifying.
"I made some changes to the car and so far it feels relatively good," Hamilton said. "I might make some more tweaks tonight and hopefully tomorrow's going to be good."
Force India driver Sergio Perez was an impressive third fastest despite brake problems which ended his night early. The Mexican pulled into the pits with about 20 minutes of the evening session remaining, with flames coming from his left rear wheel.
Red Bull drivers Daniel Ricciardo and Daniil Kvyat were fourth and sixth, with the team reverting to an earlier-specification Renault engine for this race after being unsatisfied with the performance of the new-spec power train in the previous race.
Force India driver Nico Hulkenberg had the eighth-fastest time ahead of McLaren rival Fernando Alonso and Lotus driver Pastor Maldonado, who put in encouraging performances for their struggling teams.
Alonso said his prominent showing owed more to the fact that McLaren did its running on super-soft tires later in the session than other teams and said "unfortunately, I don't think we'll be ninth-fastest tomorrow."
Several drivers complained over their team radios late in the session about graining of their front tires, indicating that tire wear looms as a key factor in Sunday's season-ending race.
Toro Rosso driver Carlos Sainz Jr. was the main casualty of the session, with his car losing power suddenly and forcing him to park it at the hairpin bend early in the session, costing the team much-needed preparatory work. The team later identified the problem as being caused by a fall in oil pressure.