"I have a problem in the engine, it's not pulling any more," the Dutchman, who will replace Jean-Eric Vergne next season, radioed to his team as he hit trouble. "I have smoke out of the engine. What should I do?"
It was a rude introduction to Formula One for the Dutch 17-year-old, who is the son of ex-F1 driver Jos and whose entry in the sport has sparked much debate.
Verstappen turned 17 on Tuesday and is almost two years younger than the previous record-holder Jaime Alguersuari, who was 19 years and 125 days when he contested the 2009 Hungarian Grand Prix. Verstappen has been competing in this year's European Formula Three season. He racked up the necessary mileage to qualify for a FIA licence in a test earlier this month.
Meanwhile Rosberg lapped 0.151 seconds ahead of Britain's Hamilton, who leads the German by just three points in the championship standings with five races left.
Spain's two-times world champion Fernando Alonso was third quickest for Ferrari and the only driver to come within a second of the two Mercedes, with Finn Valtteri Bottas fourth for Williams, ahead of countryman Kimi Raikkonen in the second Ferrari.
Danish driver Kevin Magnussen was sixth in his McLaren, two places quicker than teammate Jenson Button of Britain.
Australian Daniel Ricciardo again outperformed Red Bull partner and four-time defending world champion Sebastian Vettel, by posting the seventh quickest lap.
Germany's Vettel, runner-up behind Hamilton in the last race at Singapore, was ninth fastest, 2.225 seconds off the pace set by Rosberg. Russian Daniil Kvyat rounded out the top 10 in the first of the Toro Rosso cars, two places ahead of his temporary team-mate Verstappen.
The sun came out for the first free practice but race organisers are anxiously monitoring the progress of a typhoon gathering intensity off the Japanese mainland.