Vettel, who has already clinched his fourth straight F1 title, enters the finale with a chance to equal Michael Schumacher's 13 victories in a year and match the record of nine consecutive wins by Alberto Ascari in the 1952 and 1953 seasons.
Rosberg timed one minute 27.306 seconds in the afternoon session at the 4.3-kilometre track in Sao Paulo, .225 ahead of Vettel and .286 in front of Webber, who is competing in his last F1 race at the Brazilian GP.
The Australian driver, who will join Porsche's endurance program, has won two of the last four races at Interlagos.
Rosberg had been fastest in the first practice session with a lap of 1:24.781, when track conditions were better.
"I had a good start into the weekend, I was very quick in the rain," said Rosberg, who won twice this year and is sixth in the drivers' championship. "I have higher hopes now that perhaps we can give Red Bull a hard time this weekend."
Rosberg's Mercedes teammate Lewis Hamilton was second and Vettel was third in the morning despite briefly running off the track near the end of the session. Hamilton spun and recovered in both sessions.
It rained heavily in the afternoon and drivers couldn't switch to intermediary tires until the final minutes.
"We were working on understanding the tires in both conditions today (Friday)," Webber said. "We had the full wet and intermediate tires on the car and we did quite a few laps. It was a productive day in preparation for tomorrow (Saturday), as we expect some more wet conditions."
More rain is expected for Saturday's qualifying run and maybe for Sunday's race.
"We all know that the weather plays always a big role here at Interlagos and can catch you out," Rosberg said. "We were not able to run that much but the track feels really great and it was great fun to be out there and find the limit in these difficult conditions."
Vettel was the only driver to test the prototype dry weather tires that will be used by teams in 2014. Vettel ran a lap with them in the first session despite the damp track, but it was enough to give engineers at least some information that might be useful for next season.
"We knew it would be wet today (Friday) and might be tricky. It was good to get a bit of a base line in these conditions. We need to be sharp for the next two days and make the right calls. The main loss from the rain was that we didn't run on the 2014 tires."
Teams and drivers know little about what to expect next year because the series will go through a major change in engine rules, switching from the current 2.4-litre V8 units to a 1.6-litre V6 turbocharged engine, a move that will demand significant alterations in the design of cars.
The Brazilian GP marks the last race before several driver changes at some of F1's top teams. World champion Kimi Raikkonen of Finland leaves Lotus for Ferrari, where Felipe Massa lost his ride before joining Williams. The Brazilian replaces Pastor Maldonado of Venezuela, who could be up for the Raikkonen seat at Lotus.
McLaren will replace Mexican Sergio Perez with rookie Kevin Magnussen of Denmark, and Australian Daniel Ricciardo, from Red Bull's sister team Toro Rosso, will replace Webber.
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