While Ferrari's Fernando Alonso pushed the Briton off the top of the afternoon timesheets, Hamilton's morning time remained the quickest on an overcast and showery day in the Mediterranean principality.
The winner of the last four races, all of them one-two with team mate Nico Rosberg, had been seen jogging into the paddock minutes before the opening session started.
"I overslept," he told reporters later.
Despite the unscheduled lie-in, with Hamilton enjoying a rare weekend sleeping at home, the 2008 world champion lapped the sinuous street circuit with a best time of one minute 18.271 seconds.
"The car is still a work in progress but it felt really good out there today," he said.
"I just love racing here; this track is one of the coolest ever, and it was great to see all of the fans here already enjoying themselves.
"It's such a classic race, and I've been trying to win here again since 2008, so I'm hoping this is the year as we have such a great car."
Alonso, who has not won a grand prix in more than a year, led the second session with a best time of 1:18.482 with Hamilton second in 1:18.901.
A heavy downpour between the sessions left the track soaked and slippery, with the top drivers leaving it late to set any meaningful times.
Rosberg, winner from pole position last year, was a mere 0.032 slower than his Mercedes team mate in the morning but his times after lunch were unrepresentative and he was 20th.
"It seems that we are looking very quick here again, although our main competitors seems to be a little closer to us than in Barcelona," said the German.
"The conditions weren't great this afternoon so I didn't take any risks as there was nothing to learn on the wet parts of the track."
Australian Daniel Ricciardo was best of the rest for champions Red Bull in third place in the morning and team mate Sebastian Vettel, the quadruple world champion, filled that slot in the afternoon.
Hamilton leads Rosberg by three points in the standings after four successive one-two finishes. Mercedes have won every race and started them all from pole.
Alonso, a past winner in Monaco with Renault and McLaren, had been boosted before the session by a statement from Ferrari president Luca Di Montezemolo assuring him of the team's complete support.
Ferrari have been struggling to match the pace of the Mercedes this season and have not won in Monaco since Michael Schumacher in 2001.
The only incident of the morning was German driver Adrian Sutil, who made contact with the barriers at Mirabeau. Marussia's Max Chilton also stopped on the track.
Sweden's Marcus Ericsson nudged the wall in the afternoon, without major damage to his Caterham.
The opening session was closely watched for signs of how the new cars, with their heavier V6 turbo hybrid power units, would handle the layout with more torque and less downforce.
Some drivers have warned that Monaco could be the toughest test of the season, with the cars slipping and sliding more around the tight corners.
"Mercedes have been quite strong here over the last couple of years but it's an opportunity," said Red Bull principal Christian Horner said.
"We've got a bit of funny weather this weekend and we'll do everything we can."
The noise, or lack of it, was also much discussed with the new cars sounding far more muted even in the bowl-like surroundings of the harbour.
The loudspeakers blaring out live commentary around the track were more deafening close up than anything coming from the muted V6 turbo hybrid power units that have replaced the screaming V8s.
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- Nico Rosberg
- Fernando Alonso