The German's 1m14.378s lap was nearly seven tenths of a second clear of the rest of the field, although the latter part of the session was interrupted by crashes for Felipe Massa, Romain Grosjean and Adrian Sutil, causing two red flags.
Massa's accident was the first and the biggest.
He locked up his Ferrari's front wheels at the start of the Sainte Devote braking area, slamming into the barriers on the left-hand side approaching the corner before going into the wall on the outside of the turn. The Brazilian got out unhurt.
Shortly after the restart, Sutil lost control of his Force India through Massenet, sliding sideways into the wall.
That did not require a stoppage to clear up, and in the gap between incidents that followed, Grosjean was one of the few to get a quick time in, jumping to second.
But on his final run the Lotus driver braked too late into Sainte Devote after possibly being distracted by Lewis Hamilton's Mercedes rejoining from the pits.
Grosjean slid sideways into the barriers in a repeat of his Thursday crash.
With only a minute of the session remaining, the red flag brought the morning to a close.
Rosberg managed to get a sublime lap in between the shunts, moving comfortably clear of the field despite clouting the barrier at Portier as he got his Mercedes sideways out of the corner.
Grosjean retained second, ahead of Sebastian Vettel - who had been quickest before the field switched to super-softs, but encountered traffic on a potentially quick late run.
Fernando Alonso's Ferrari and Hamilton completed the top five.
Kimi Raikkonen had a harmless trip down the Mirabeau escape road before taking sixth, followed by Mark Webber, Paul di Resta, Pastor Maldonado and Nico Hulkenberg.
- Sports & Recreation
- Romain Grosjean
- Felipe Massa
- Adrian Sutil