The German, who is fighting for second place in a championship already won by team mate Lewis Hamilton, lapped the Hermanos Rodriguez circuit with a best of one minute 21.531 seconds.
"It feels like a kart circuit with a lot of very tight corners and the two stadiums are really spectacular with all the fans," said Rosberg.
Red Bull's Daniil Kvyat and Daniel Ricciardo were second and third on the timesheets with rain falling later in the afternoon.
Toro Rosso's Max Verstappen, who was not even born last time Formula One raced in Mexico in 1992, brought out red flags with a crash at the final corner in the afternoon after setting the pace in the morning session.
The 18-year-old Dutch driver was still the youngest driver to top a Formula One practice session with a best effort of 1:25.990.
He appeared to cut a corner on the Esses sequence in doing so, however.
Russian Kvyat, born two years after Britain's Nigel Mansell won the 1992 race, was also second fastest in the morning.
Hamilton, who took his third world championship and 10th win of the season in Texas, was 11th and fourth fastest respectively.
"It was really challenging out there today - for everyone I think - but also a lot of fun," said the Briton.
"It's crazy how slippery it is. Because we're so high up in terms of altitude, there's even less grip than in Monza, so the car was just sliding around."
Rosberg, chasing Ferrari's Sebastian Vettel for second with three races remaining, was sixth before lunch when his car's rear brakes overheated. The German headed back to the pits with flaming wheels.
Vettel was fourth in the morning and then fifth fastest.
Mercedes have also won the constructors' championship, leaving Sunday's race with nothing to play for other than the race win and precious points for those further down the standings.
The high-altitude circuit, much revamped from the old one with the daunting Peraltada curve now cut in half, has one of the longest straights on the calendar and Friday's start to practice was in damp conditions.
"The cars were sliding around and sometimes you felt more like being in rallying than in Formula One," said Ferrari's Kimi Raikkonen, who has experience of both series.
Spectators queued outside from early on, amid a heavy police presence and the usual traffic gridlock, to get a glimpse of the cars and home favourite Sergio Perez.
Mexico's only current Formula One driver, who is likely to be joined on the grid by Esteban Gutierrez next season with new team Haas making an announcement later, was ninth and 15th fastest in the sessions.
(Editing by Mark Meadows/Peter Rutherford)
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