It was the 30-year-old Briton's first success on the streets of his favourite circuit and came at the ninth attempt as he outpaced Rosberg in a tight contest to claim the 43rd pole of his career.
"It has been a long, long time," said Hamilton. "I can't express to you how happy I am. It was not the easiest session. There were a lot of things that throw you off your rhythm and I did not have that rhythm until the last couple of laps.
Hamilton clocked a final best lap in one minute and 15.090 seconds to wind up three-tenths of a second clear of Rosberg and fellow-German Sebastian Vettel, who was third for Ferrari ahead of the two Red Bulls of Australian Daniel Ricciardo and Russian Daniil Kvyat.
Rosberg said: "It was the other way round for me. I knew Lewis was quick and it didn't work out for me."
Hamilton struggled to find his best form through the first two parts of qualifying before hitting his rhythm in the final top-ten shootout.
Rosberg was quickest in the first two mini-sessions, but made minor errors under pressure when he twice locked up at the Ste Devote corner.
Hamilton's success ended Rosberg's hopes of claiming a hat-trick of three successive poles in the Mediterranean principality and gives him a good opportunity to stop the German recording a third straight win in Sunday's classic 78 laps race.
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