Rosberg's fastest lap was just 0.072 seconds ahead of Hamilton but the German dealt a psychological blow to the Briton ahead of Saturday's qualifying sessions.
Rosberg leads the overall standings by 23 points after Hamilton's catastrophic engine failure in Malaysia
left him fuming.
Hamilton, the world champion in each of the last two seasons, was leading the race at Sepang when his engine blew on the 41st lap, allowing Rosberg to take third place and a lead in the overall driver standings.
Hamilton described the pain of the failure as "indescribable" and demanded answers from his team -- though he later used his Twitter account to praise them for their hard work.
He vowed to fight back and on the official Mercedes website he added: "The guys are hurting from what happened too and I know they'll be working just as hard to get things right next time."
Hamilton appears to have lost some focus after the incident, playing with his phone during a press conference in Japan -- adding bunny features to himself and rival racers on Snapchat instead. His obvious amusement and behavior drew much criticism on Twitter.
"Today was meant to be fun, not at all disrespectful," Hamilton posted on Twitter after the incident. "Some people take themselves to (sic) seriously. I had a blast, highlight of my day!" he said.
"Re press conference, it's been the same for 10 years. It's not the media or mediator, it's the format. Fans should be asking the questions!!"
Rosberg will be looking to avenge last year's defeat in Japan, where his Mercedes teammate beat him in a duel in the first two corners to take the lead and win the race.
Hamilton faces daunting task
With only four races left after this weekend, the British driver faces a tough task to hold on to his title.
Rosberg was cautious with his words after the practice session.
"It's been a case of finding my way today," he said on the F1 website.
"However, on the soft tire we showed strong one-lap pace, the balance felt good and the track was really exciting to drive."
Hamilton was more upbeat after his disappointment at Sepang.
"It's been a really good day with no problems on the car which is great," he said. "It's great to be here in Japan and I'm excited to get out on track again for qualifying tomorrow."
Could rain affect Suzuka race?
Red Bull's Max Verstappen
continued his good form Friday. The 19-year-old split the Ferraris during practice, finishing with the fourth fastest time, sandwiched between Kimi Raikkonen in third and Sebastian Vettel in fifth.
The two Force India drivers Sergio Perez and Nico Hulkenberg finished in sixth and seventh.
So far, the drivers have enjoyed dry weather but the championship outcome could yet be influenced by wet conditions with rain forecast for qualifying and possibly the race.