Rosberg, winner from pole for the past two years on the twisty metal-fenced streets where passing is almost impossible, qualified second in an overcast final session with rain threatening.
"It's been a long time," said an elated Hamilton, whose only win in Monaco came in his 2008 championship year with McLaren from third place on the grid.
"It wasn't an easy session...I didn't have the rhythm until the last two laps.
"This is incredibly special for me," added the Monaco resident, well aware the race has been won from pole for the last six years, of his 14th successive front row start and fifth pole in six races.
Rosberg's hopes disappeared when he locked up the front wheels at the Sainte Devote corner at the start of his abandoned final quick lap to leave Hamilton 0.342 seconds faster.
"I just lost touch a little bit there towards the end. Of course you are going for it because you have to...it didn't work out, that's it," said Rosberg.
Sebastian Vettel will start third for Ferrari on Sunday, after struggling to get heat into his tyres, with his former Red Bull team mate Daniel Ricciardo alongside him on the second row.
"Overall it was a good session and our aim now is to have a good race tomorrow and try to split the Mercedes," said Vettel, whose grid place was Ferrari's best in Monaco since 2009.
Dutch 17-year-old Max Verstappen qualified an impressive 10th for his first Monaco Grand Prix with Toro Rosso, and will start ninth after his Spanish rookie team mate Carlos Sainz was ordered to start from the pit lane.
Sainz, who had qualified in eighth place, paid the price for failing to stop for weighing during the first stage of qualifying.
Russian Daniil Kvyat qualified fifth for Red Bull, ahead of Ferrari's Kimi Raikkonen and Mexican Sergio Perez in a Force India.
McLaren's 2009 champion Jenson Button qualified 12th but will move up to 10th thanks to Sainz's penalty and also a five place demotion for Frenchman Romain Grosjean who had an unscheduled gearbox change.
Button's team mate Fernando Alonso, who predicted earlier in the week that McLaren could score their first points of the season on Sunday, qualified 15th but will also move up two places.
There was disappointment for Mercedes-powered Williams and Finland's Valtteri Bottas, who qualified only 17th with Brazilian team mate Felipe Massa 14th.
(Reporting by Alan Baldwin, editing by Ken Ferris and Toby Davis)
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