Alonso, third overall in the championship, clocked 1 minute, 18.482 seconds. Hamilton was .419 seconds behind, and Sebastian Vettel .535 behind for Red Bull. Frenchman Jean-Eric Vergne was fourth best for Toro Rosso.
Spectators waited for nearly 40 minutes as drivers stayed in their garages until the track dried after some showers.
Hamilton was fastest in the morning session ahead of Mercedes teammate Nico Rosberg, and Red Bull driver Daniel Ricciardo.
There is a final practice session on Saturday morning before qualifying in the afternoon.
Hamilton, who has won 26 races, has never started from the pole in Monaco despite securing 35 career poles elsewhere.
"It felt really good out there today. I had a good first session and was then really pleased to get those last few laps in the dry this afternoon," Hamilton said. "I'm feeling pretty set for Saturday. There is still some work to do, but we have tomorrow to look into that."
The British driver is confident he can end his barren run in Monaco, where he has not won since 2008, the year he won the F1 title.
"This track is one of the coolest ever," Hamilton said. "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."
Hamilton has four poles this season, with Rosberg clinching the other, meaning Mercedes have swept all five races and all five poles.
Hamilton has won the previous four and Rosberg took the opening GP in Australia, where Hamilton retired with engine failure.
Rosberg, who secured his maiden Monaco GP win last year, trails Hamilton by three points overall.
"It seems that we are looking very quick here again, although our main competitors seem to be a little closer to us than in Barcelona," the German said. "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."
Monaco's tight, sinewy circuit makes overtaking almost impossible and puts whoever gets pole into a prime position.
But given that engine power is less important than at other races, Red Bull could end Mercedes' winning streak if Vettel or Ricciardo can upstage Hamilton and Rosberg in qualifying.
"The nature of the circuit doesn't put such a premium on straight-line performance, which has obviously been our weakness this year. We're hoping to give these guys (Mercedes) a run for their money," Red Bull team principal Christian Horner said. "It's been an encouraging start to the weekend. When you consider where we were preseason, we've come a long way in a couple of months."
Vettel was fifth fastest in the first practice behind Alonso.
The Spaniard is 51 points behind Hamilton but four ahead of Vettel, his main rival from previous seasons, who is fourth.
In the morning's run in overcast, chilly conditions, British driver Max Chilton spun off in his Marussia car, while struggling German driver Adrian Sutil stalled his Sauber.
Swedish driver Marcus Ericsson slammed his Caterham into the barriers with a minute remaining in the afternoon run.