The Mercedes duo traded places at the top of the timesheet before Hamilton asserted himself with the fastest time of the session roughly halfway through.
Rosberg was fastest of all in the first sector of the lap, but his later efforts to topple his team-mate fell short by less than half a tenth of a second.
Daniel Ricciardo interloped in this personal battle by briefly going fastest in the early part of the session, and he was one of only two other drivers to ultimately lap below 1m19s.
The Australian looked to have Red Bull's RB10 hooked up nice an early and he wound up third fastest, less than a quarter of a second slower than Hamilton.
That bumped world champion Sebastian Vettel to fifth. The German took a while to find his own groove and ended up half a second shy of his team-mate's best time.
Alonso's Ferrari team-mate Kimi Raikkonen also improved late on to round out the top six, less than a tenth clear of fellow Finn Valtteri Bottas in the best of the two Williams.
He was just under two tenths faster than team-mate Nico Hulkenberg, who complained of some braking issues and ended up just fractions of a second slower than Kevin Magnussen's McLaren.
Hulkenberg was the last man to lap below 1m20s in the session. His Force India rounded out the top 10, ahead of McLaren's Jenson Button and Esteban Gutierrez, who was an impressive 12th fastest for Sauber.
Lotus has shown improved form recently but struggled in this session, as Romain Grosjean and Pastor Maldonado could only manage the 13th and 14th fastest times.
Felipe Massa also struggled in the second Williams, winding up 16th fastest behind Jean-Eric Vergne's Toro Rosso.
There were suggestions ahead of the event that Monaco might present the toughest challenge of the season to the drivers, but there were only a handful of significant incidents.
Max Chilton's Marussia became stranded after an early spin at Mirabeau, while Adrian Sutil's Sauber struck the barrier after a spin at the same corner in the late-stages.
Raikkonen's Ferrari spun but continued at Ste Devote on his final run, while team-mate Alonso took to the escape road at Mirabeau after locking his brakes, but the Spaniard easily kept his car out of the barriers.
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