He completed 38 4.73-km laps in an FW24 in Barcelona to claim a personal best time of one minute 21.070 seconds on lap 29 and finished eighth fastest overall, despite a spin.
"It was sensational," said an exhilarated Rosberg. "Now I don't want to drive anything else.
"The first laps were like a game with a playstation -- everything went so fast and seemed so unreal.
Nico's father, who won the world title driving for Williams, was at trackside with friends to witness his son making history on his Formula One testing debut.
"My father had advised me not to attempt too much and just enjoy the whole experience. I think I managed to do that quite well," said the young Rosberg, who was born on 27 June 1985.
Rosberg's run was part of his prize for winning Williams' engine suppliers BMW's junior race category title in Germany.
The youngest driver to race in Formula One was Mike Thackwell of New Zealand, who was 19 years and five months old when he raced in Canada in 1980.
Britain's Jenson Button became the youngest driver to score points in Formula One with sixth place in Brazil in 2000.
The Australian set a best time of one minute 18.177 seconds, just 0.094 ahead of Colombian Montoya.
Webber's Jaguar team mate, Brazilian Antonio Pizzonia, failed to record a time after crashing in the morning.
Pizzonia spun off at the second corner and, according to a team spokesman, caused "extensive" damage to his car.
Last Thursday, Pizzonia rolled and wrote off one of Jaguar's top-of-the-range road cars, a $70,000 (£45,000) S-Type, while driving reporters around the circuit.
McLaren's test driver, Austrian Alex Wurz, was third fastest, and the only driver to join Webber and Montoya in the one minute, 18-second bracket.
Spain's Fernando Alonso, who has taken over at Renault from Briton Jenson Button, was sixth fastest.
Renault also gave Romain Dumas his first F1 test and the French youngster was 11th overall.
BAR's Anthony Davidson, who twice raced for Minardi this year, was seventh fastest, while fellow Briton Gary Paffett, the German Formula Three champion, was ninth for McLaren. He will test for the team again on Thursday.
Champions Ferrari, who tested with Italian Luca Badoer alongside Jaguar, Toyota and BAR at Barcelona last week, have been in action alone at Italy's Mugello circuit -- this time with Brazilian Luciano Burti driving.