The German, who celebrated his 28th birthday on Thursday, clocked a best lap of one minute and 32.248 seconds in improving drying conditions after a rainswept morning.
That time was enough to lift the Monaco Grand Prix victor almost three-tenths of a second clear of nearest rival Mark Webber of Red Bull.
“The afternoon went well,” Rosberg said. “On one lap I think the car is still quick, as we have seen in the last few months, so qualifying should be OK.
“Then the only question mark is our race speed. We practised for the race speed today. It seemed to be OK, decent, but I'm sure it’s still going to be a little bit of a problem for us. The next thing is that it's going to be another 10 degrees more tomorrow and Sunday and that could completely change the picture again,” he added.